The paper book

The regime-split test (s4) reporting 'stable: true' is taken at face value, but no per-regime correlation values were shown, so it is treated as unverified rather than confirmatory.

No material new geopolitical or OPEC+ supply shock is assumed between as_of and horizon, since none is reflected in the data provided.

d2/d3/d4 represent COT-type positioning/open-interest metrics; exact units are not fully specified in the data provided, which is itself a limitation.

d1 last value (90.23 on 2026-10-01) is the correct starting point for the 33-day horizon to Nov 3, 2026.

Kalshi mid is informative of market consensus

No major unscheduled supply shock beyond what's in d3's current trend

d6 reflects positioning/crowding, not unrelated noise

Resolution is a close-level threshold check

d2 is the relevant WTI daily log-return series and current vol regime persists over the horizon

No regime change (no OPEC+ supply shock, no major geopolitical event) is assumed beyond what's embedded in current volatility; this is explicitly uncertain.

33 calendar days ≈ 23 trading days to horizon.

Resolution is interpreted as WTI close on/near 2026-11-03 being >= 93.99 (terminal level test), consistent with the Kalshi contract naming (T93.99) and 'on Election Day' framing.

d3 is the daily log-return series of d1 (near-zero mean, sd 2.9%), appropriate for a random-walk diffusion model given ADF confirms unit root in levels (s4).

d1 is the daily WTI closing price series; last observation (90.23 on 2026-10-01) is the current level.

No major supply shock or geopolitical event is modeled beyond what is embedded in historical volatility.

s3's underlying return series is a reasonable proxy for WTI's own 33-day return distribution.

d1 is WTI front-month close and 90.23 on 10/1 is the correct starting point.

The regression in s4 relating tx_hdd_anom to price changes is for a dependent variable not explicitly confirmed to be WTI itself (r2 only 5.3%, DW=0.12 indicates severe residual autocorrelation even after HAC correction) — treated as weak, tangential evidence only.

Treating the 33-day-ahead price change as approximately normally distributed (random walk, no explicit drift) is a simplification; a non-zero drift (positive or negative) is plausible but unmeasured here.

Daily WTI log-returns over the next ~23 trading days behave approximately like the last 5 observed days in volatility (~2.27% daily sd) — no explicit longer-run return series (d2) was decomposed into a horizon-matched forecast.

Price process is treated as non-stationary/near-random-walk per s4, so no strong mean-reversion assumption is applied.

No explicit futures curve (contango/backwardation) data was provided; I rely on general 2026 domain knowledge of a well-supplied global oil market (OPEC+ unwinding cuts, non-OPEC supply growth) as a qualitative anchor, not a quantified input.

d5's exact definition (likely a positioning or flow-related weekly series) is not fully specified in the data; I treat its persistent negative sign as a mild bearish signal but with low confidence on interpretation.

d2 and s3's underlying return series are daily WTI log/pct returns used to construct the 33-day bootstrap.

The 'Election Day' framing is a calendar convenience, not evidence of a causal link between US elections and WTI level; treated as a naming artifact rather than a fundamental driver.

Daily return sd (d4/d5, ~1.1-1.5%) is roughly stable over the 40-day horizon, giving ~7% terminal-return sd via sqrt(t) scaling, used only as a rough sanity check.

No structural break (OPEC+ surprise, geopolitical shock, election-driven policy shift) occurs between 9/24 and 11/3 that current data cannot anticipate.

No major volatility regime shift between now and Nov 3

Log-returns are approximately i.i.d. normal over the horizon

No major scheduled OPEC+ or geopolitical event between now and Nov 3 is assumed beyond what's already reflected in current price/vol.

d3-d6 represent futures positioning/OI, implied vol, and volume proxies for WTI derivatives, used only qualitatively as crowding signals since labels are not given explicitly.

Daily log-return statistics from d2 (full sample, ~3.54% daily sd, near-zero autocorrelation) are a reasonable proxy for near-term realized volatility.

The resolution reflects WTI closing price on/near 2026-11-03 rather than a continuous path-dependent barrier (since spot is already >85.99, a barrier interpretation would make this trivially near-certain).

Kalshi mid price (0.55) reflects a liquid, informationally efficient consensus, not a stale or thin quote.

WTI close on 2026-09-24 (93.39) is the effective starting point 40 calendar days before Nov 3; trading-day horizon is roughly 27-28 sessions.

The bootstrap (s3) resamples historical daily log-returns with realistic block/path structure to build a 40-day return distribution; I treat it as the best available conditional forecast despite not seeing its exact resampling method.

Daily WTI return series (d2) is representative of the return-generating process likely to persist over the next 40 trading days, i.e., no unprecedented regime break (war, OPEC surprise, recession shock) beyond what's in the 2-year sample.

Bootstrap resampling (s3) drawn from the trailing ~344-day return sample is a reasonable proxy for the next 40 trading days' distribution.

No structural regime break (e.g., OPEC+ supply shock, major demand collapse, or geopolitical de-escalation) between 9/24 and 11/3 that isn't reflected in the historical return distribution used for bootstrap.

WTI.close 'over the horizon' is interpreted as the terminal/settlement-date close near Nov 3, not a max-over-window touch condition (if it is a touch condition, probability of YES is materially higher since spot is already above strike today).

No confirmed heating-demand (HDD) data available (d5 failed) — winter demand impulse into Nov 3 is unmodeled

Resolution is based on the WTI close on/near Nov 3, 2026, not a continuous 40-day touch condition

d4 (n=2: 0 then 30) is treated as a tropical storm/outage activity indicator; too sparse to be reliable but directionally consistent with a recent Gulf supply-side shock

d3 is treated as an oil-implied-volatility-like proxy (range 15.8–52.6, mean 33.56) reflecting market-implied uncertainty

d2's large mean/sd (0.037/0.196) is inconsistent with daily WTI log-returns and more likely reflects a related but different series (e.g., a spread or weekly change) — I do not use it as WTI vol input

d1 represents the WTI daily close price series (level, non-stationary per s5)

No structural break (e.g., large supply-shock resolution or war de-escalation) between now and Nov 3 is assumed beyond what's embedded in the historical return distribution used for the bootstrap.

The Sep 24 price of 93.39 is a genuine settled close, not a data error, despite the large day/day swings in the preceding week (101.9 -> 89.84 -> 93.39).

d2 represents WTI daily log returns; d3 represents COT percent-of-open-interest (net length) used in s5; d5 represents weekly EIA-style crude inventory levels (barrels).

Resolution is based on WTI closing price on/around Nov 3, 2026 (terminal condition), not a continuous barrier that price must never breach during the 40-day window.

d4 (n=1, constant=0) appears to be a degenerate/placeholder series that cannot support any claim made about it

The market mid of 0.51 already prices whatever public information exists as of 2026-09-19; I have no information edge over it from this data package

No test isolating an 'election day' or event-specific effect was successfully run (t7: n=0 events in sample) — the resolution date's significance to the price process is unverified

d1-d8 are unlabeled proxy series whose direct causal or definitional link to the WTI close level was not established in the material provided

d4 (mean 36.9, range 15.8-95, last values 22-31) is plausibly a temperature or CDD/HDD-adjacent series but its exact units/location are not specified in the handle description, so I treat it as corroborating rather than load-bearing.

houston_gust/lakecharles_gust/portarthur_gust in t7 are Gulf Coast wind-gust proxies tied to storm intensity near refining and port infrastructure (Houston Ship Channel, Lake Charles, Port Arthur).

d2/d3 binary series (mean ≈0.02-0.03, sparse 0/1 flags) represent storm watch/warning or landfall event indicators used as the trigger for t6's event study.

WTI spot is trading near the $92 strike as of 2026-09-19 given the market's near-50/50 pricing (I cannot back out the exact spot level from the supplied handles, only return/CAR-style series).

d4, d5, d6, d7 could not be reliably identified/interpreted (no clear labels), so I gave them low weight beyond noting the (weak, high-residual-autocorrelation) t8 regression and the (robust) t5-t7 correlations confirming WTI moves with broader risk-asset factors, not in isolation.

No major scheduled OPEC+ decision, sanctions escalation, or macro shock between 2026-09-19 and 2026-11-03 is modeled; I have no data confirming or ruling out such an event.

d3 is a reasonable proxy for WTI's daily log/percent return volatility despite some day-by-day inconsistency versus d1's level changes, likely due to timing/definition mismatches in this abstracted dataset.

The Kalshi contract settles/checks WTI's close on or near 2026-11-03 against a single 91.99 strike (a level check at a point in time), not a path-dependent min/max condition over the full 45-day window.

No walk-forward or out-of-sample backtest was actually run on d4's drift; the significance claim is a static in-sample t-test only, which I explicitly discount for that reason.

d6's high persistence (autocorr_1=0.975, t5) and tight bootstrap CI (t6: [0.088,0.117]) suggest a distinct, structurally different (bounded, mean-reverting-slow) series, possibly a spread/probability/positioning metric — I could not confidently identify it, so I did not incorporate it into the price forecast.

d1/d2 (highly correlated, corr=0.98, t3) are treated as two co-moving level series (possibly price and a related benchmark) exhibiting the same non-stationarity documented in t1; I do not use them for level forecasting given t1's unit-root finding.

d4 is interpreted as the relevant WTI (or WTI-linked) daily log-return series given its scale (mean 0.23%, sd 2.19%/day) is consistent with oil's historical daily volatility; no series in the package matches the ~$92 price level directly, so no level-based backtest was possible.

Resolution is based on a single closing print at or near Nov 3, not a path-dependent barrier condition, per the stated rule 'WTI.close level >= 91.99 over the horizon.'

No new macro catalyst (OPEC+ decision, major geopolitical event, US election-related energy policy shock) occurs between 9/19 and 11/3 that is not already reflected in current positioning data.

d2/d6 behave as open-interest/volume-like crowding proxies and d8 as a funding/basis-like sentiment proxy, based on their described units and comovement with price -- exact identity not confirmed.

d7 is the WTI daily log-return series and d1 is the WTI price level series (handles inferred from context, not explicitly labeled in the prompt).

45 calendar days horizon approximates to ~31 trading days for vol scaling.

No knowledge of any market-moving event after 2026-09-19 is assumed or used.

d7's move to near its historical minimum reflects positioning (e.g., net short building or hedging flow) rather than a bullish signal in itself; its regression relationship to price (t5) is too statistically fragile to rely on.

d3/d4/d5, highly intercorrelated (t3 corr=0.82) and rising ~2x their sample means over the same window, are cost-of-carry/positioning proxies that move with acute tightening episodes.

d1 and d8 are volatility/event-risk type series (not raw price) whose recent multi-day climb toward historical extremes (d1: 2.83→3.51 over last 6 sessions vs. mean 2.357, max 3.772; d8: 12.7→33.2 over last week vs. mean 0.527, 95th pct 6.91) reflects a real, still-unfolding physical/market stress event rather than a data artifact.

Kalshi's 0.51 mid implies the $91.99 strike is close to the current market-implied forward WTI price for Nov 3 (near-ATM).

The 45-day horizon and Nov 3 2026 date appear to be an arbitrary snapshot choice with no covariate in the dataset tied mechanistically to the U.S. election.

t5's 'stable' regime-split label is taken at face value from metadata since no per-regime correlation values were reported alongside it.

No historical WTI price-level base rate data was provided by the tools; the base rate below is a rough domain-knowledge prior, explicitly flagged as such, not a tool output.

d1–d5 are unlabeled series; I cannot verify what they measure (spot price components, positioning, volume, sentiment, etc.), which limits causal interpretation to structural/statistical properties only.

The horizon resolves on the Nov 3 close specifically (or a level check at/near that date), consistent with 'WTI.close level >= 94.99 over the horizon.'

No major scheduled OPEC+ or macro catalyst between 9/19 and 11/3 is assumed beyond generic hurricane-season tail risk (not separately quantified in the provided data).

d3-d7 are plausible daily change/return series usable to proxy realized volatility (sd ~1.1-1.5 in the relevant units) even though their exact construction is not labeled.

d1 is the WTI settlement/close series referenced by the resolution rule.

45 calendar days approximated as ~31 trading days

d1/d2 are WTI level and daily log return respectively

No maturity-specific term structure (contango/backwardation) or seasonal Nov-election effects are captured in this dataset

The market's 0.47 price implies spot is close to the $94.99 strike (a necessary condition for a near-coin-flip price under EMH), which I cannot independently verify from the handles

d2 is the corresponding daily log-return series for d1 (sd=2.454%, consistent with a plausible commodity daily vol)

d1 is the relevant price/level series (or a monotonic transform of it) underlying the WTI resolution variable, though its raw units (1.68-3.77 range) are not confirmed to map cleanly to a $95 WTI price

d3 is treated as a volume proxy; its recent decline (3.99e5 -> 2.17e5 over 9/11-9/18) is read as fading participation after the spike.

d6 is treated as a sentiment/positioning proxy (crowding signal) given its freshness through the as_of date and z-score-like scale; exact construction is unknown.

d2 is the daily log-return series used for the volatility scaling in the random-walk projection.

Resolution is interpreted as WTI close specifically on 2026-11-03 (matching the Kalshi ticker KXWTI-26NOV03-T94.99), not literally 'any close during the 45-day horizon >=94.99' -- the latter reading would make the question near-certain YES already given spot is already above strike, inconsistent with a 0.47 quote, and is treated as templating artifact rather than the true rule.

d4's regression/correlation results (t6, t7) are treated as uninformative for current dynamics because the series stopped updating in mid-July 2026, well before the current price shock - this is a data-quality gap, not evidence of 'no relationship.'

d5 is a volatility-type proxy (magnitude and jump pattern consistent with an implied- or realized-vol index) rather than a price series, given its 14-127 range and lack of correlation with the stale d4 return series (t6, t7).

The resolution is interpreted as the terminal close on/near Nov 3, 2026 (Election Day) being >= 94.99, not a path-dependent 'ever touches' condition; if the rule is path-dependent, true YES probability would be materially higher than my point estimate since price only needs to clear threshold once during the window.

d1 is the WTI (or a closely tracking crude benchmark) daily price/close series; d3 is its daily log/simple return series.

No scheduled macro/OPEC/EIA event is known as of 2026-10-12 02:30 UTC that would be a clear catalyst (none provided in data).

Kalshi settlement tracks the CME WTI futures daily settlement closely enough that no basis/rounding issue flips the resolution near the threshold.

d2's daily-return distribution (n=39) is representative of near-term volatility regime, not itself an artifact of a stale/different window.

Last close (90.12 on 2026-10-12, from d1) is the correct pre-settlement reference price for the Nov26 contract.

No Kalshi-specific order book, open interest, or funding data exists in this dataset; thus true market-implied probability cannot be directly observed and must be proxied by statistical modeling of the underlying.

The 81-observation daily return sample (d2) is representative of the current volatility regime and no regime shift occurred between d1's last print and the as_of timestamp.

WTI Nov26 contract settlement tracks spot/futures price series d1 closely enough that d1's last value (90.12) is a fair proxy for the pre-settlement reference price.

ADF test (s4) confirms returns series is stationary, supporting use of unconditional historical return distribution for short-horizon forecasting.

No major scheduled catalyst (OPEC meeting, EIA inventory shock, geopolitical event) between 10/12 and 10/13 is assumed beyond what's embedded in historical volatility; this is NOT verified with an event calendar.

Daily return series d2/d3 (and their stats s2,s3,s5,s6) are representative of the return-generating process still in effect for this specific 1-day window (no regime shift specific to Oct 13).

The d1 last value (90.12 on 2026-10-12) is the correct most recent settlement/reference price for the November 2026 WTI contract used as the base for the Oct 13 move.

No material geopolitical or OPEC supply shock between 2026-10-12 and settlement is assumed absent from the data provided

d5 (volume) anomaly on 2026-10-12 (2.2e4 vs ~3e5 typical) reflects a data/holiday artifact and does not itself signal a large directional move

d4 is a correlated macro/dollar factor (corr=0.554 with d1 per s3) used as directional cross-check, not primary driver

d3 is an implied-vol-like series (~7-9%) used only as a sanity check on realized vol, not directly priced into the 1-day distribution

d2 is the daily log-return series for WTI (or a closely correlated proxy) consistent with d1 level moves

WTI Nov26 contract settlement tracks the spot/futures series represented by d1 closely enough to use its level and return stats as proxy

insight:ins_01M3ZV4EM46811213JGQGR is irrelevant at this 1-day horizon since it targets a 21-day forward window and is already flagged WEAK on re-test.

No OPEC+ meeting, major geopolitical event, or inventory surprise is already priced in but unobserved as of 2026-10-13 02:30 UTC.

The 61-day and 343-day historical return distributions (s2, s3) are representative of near-term volatility regime; no regime shift (e.g., new supply shock) between as_of and settlement.

Settlement price for Oct 13 is well-approximated by the most recent close (90.12) plus one incremental daily return.

d3 series (unclear units, ~7-8% range) is treated as a secondary curve/basis signal with ambiguous interpretation and is not used to materially shift the point estimate.

The drop in d4 (volume proxy) on 10/12 reflects a lower-liquidity session and does not itself signal directional information.

No scheduled macro/geopolitical catalyst specific to Oct 13, 2026 is embedded in the data provided; absent such information, the historical unconditional distribution is the best available estimate.

The Nov26 WTI futures settlement is well-approximated by the last observed daily close series (d1) and the log-return distribution in d2/s2.

No major scheduled catalyst (OPEC+ meeting, EIA inventory shock, geopolitical event) between Oct 10-13 is known to me as of the as_of date

The settlement price on Oct 13 is well-approximated by extrapolating the Oct 2-9 price series without new information

Daily WTI log returns are approximately mean-zero and i.i.d. at the 3-4 day horizon (contradicted somewhat by autocorr_1=0.887 in levels, d1, but that reflects price persistence, not necessarily predictable drift)

No major scheduled catalysts (OPEC meeting, EIA inventory shock, geopolitical event) between 10/10 and 10/13 are assumed absent from the given data; none were provided, so this is an information gap, not a confirmed absence

The November WTI futures contract (used for settlement) tracks the spot/front-month series represented in d1/d2 closely enough for this estimate

Daily WTI log-returns are approximately i.i.d. over the 2-day horizon (ignoring autocorrelation structure, though autocorr_1=0.89 for price level suggests momentum could persist)

No new macro/geopolitical shock is assumed between as_of (2026-10-10) and settlement (2026-10-13); this is explicitly untestable with current data and is a source of residual uncertainty.

Settlement mechanics: Kalshi settles to the official November WTI contract daily settlement, assumed to track the front-month price series in d1/d2 without material basis distortion over 4 days.

d3, d4, d5 are auxiliary series (possibly a related commodity/spread, implied vol term structure, and a COT-type positioning measure) feeding regression s5; interpretation of exact economic meaning is uncertain beyond their statistical role.

d2 series = daily log returns of WTI front-month (n=344, mean 0.0012, sd 0.032), used as the random-walk return generator for the 2-trading-day horizon (Oct 9 -> Oct 13, excluding weekend).

d1 series = daily WTI settlement price (USD/Bbl); last observation 91.66 on 2026-10-09 is the pre-horizon anchor price.

No major scheduled macro/OPEC/geopolitical catalyst between Oct 10-13, 2026 is embedded in the data provided; none is assumed beyond what the recent price action reflects.

The d2/d3/d5 return series are daily WTI log/pct returns at a frequency consistent with the 4-day bootstrap horizon used in s3.

Oct 12, 2026 (Monday) is a normal or near-normal trading session for NYMEX WTI futures (Columbus Day is not a full energy-market holiday).

Nov WTI contract (the underlying for KXWTI-26OCT1314-T91.99) tracks the d1 price series without a material basis divergence into Oct 13 settlement.

No major scheduled macro/OPEC/EIA event embedded in the data that would create a large directional jump is visible in the provided evidence.

d1 last value (91.66 on 2026-10-09) is the most recent pre-as_of close/reference price for the Nov 2026 WTI contract.

Oct 12, 2026 (Monday) is a normal trading day for WTI futures (Columbus Day is not a NYMEX energy holiday), so the horizon to settlement is effectively 2 trading sessions from the last observed close (Oct 9).

No major scheduled OPEC+ or EIA event is assumed to fall between Oct 10-13 beyond what's reflected in current data; this is untested.

d4's economic meaning (possibly inventory or positioning data) is uncertain; I cannot confirm its sign convention or how fast it transmits to price.

d5 is a shorter-window daily log-return series more representative of near-term dynamics than d2 (whose 5.7% daily sd seems implausibly high for WTI and may be a different/longer-period series).

d1 is the WTI Nov26 daily settlement/close price series used for the Kalshi contract.

No new macro or geopolitical shock between Oct 10 and Oct 13 is assumed as baseline; this cannot be ruled in or out from the supplied data.

d4 final observation (9975, a sharp drop from about 295000 the prior day) is treated as a probable data anomaly (thin holiday volume or data error) rather than a genuine liquidity collapse signal; if it is genuine, it could indicate thin-market risk of larger swings into Oct 13, widening uncertainty rather than narrowing it.

d2 return series does not clearly align temporally or in frequency with d1 price series (d2 n=271 vs d1 n=82), raising ambiguity about which return series actually drives d1; this is flagged as unresolved, not assumed resolved.

No access to actual Kalshi market quotes, open interest, or funding data (d5/d6 failed) — probability is inferred from underlying price dynamics only, not validated against actual market pricing.

The Oct 13 settlement behaves like the historical daily closes in d1 (no discontinuous news shock, e.g., OPEC+ surprise or geopolitical event, between Oct 10 and Oct 13).

Log-returns are approximately i.i.d. over the 3-day horizon (ignoring the observed autocorr_1=0.766 in s2, which could compound short-term momentum either direction).

The November WTI contract settlement price is comparable in construction/continuity to the historical daily closes in d1.

No major scheduled macro/OPEC/EIA event between 10/10 and 10/13 is known to me as of the as_of date that would independently resolve the ~0.44% gap.

d2's 5.7% daily sd is unusually large for WTI; treated with caution and not used directly for 4-day vol scaling.

Settlement price behaves like the last observed daily close for distributional purposes

No material scheduled news (OPEC, EIA inventory, geopolitical) between Oct 10-13 was available to condition on; none cited in data

Returns are approximately independent day-to-day for the 2-day aggregation (ignoring AR(1)=0.766 in d2, but s3 momentum beta is insignificant so no usable autocorrelation signal)

d2 return series sd (5.69%/day) is representative of near-term volatility through Oct 13

No major scheduled macro/OPEC event already priced into d1 that would create a directional jump independent of the modeled distribution.

d2/d3/d4/d5/d6 series represent returns at varying horizons (daily vs 4-day) as labeled by the stat refs (s2 matching d2, s3 as the 4-day bootstrap of the same return series).

Oct 13 is a normal trading/settlement day (Columbus Day on Oct 12 does not halt futures settlement).

d1's last value (90.59 on 2026-10-09) is the effective spot/reference price for computing distance to strike (90.99).

No major physical supply shock (OPEC+ surprise cut/hike, major outage, geopolitical event) occurs in the 3 trading days between 10/10 and 10/13 that isn't already reflected in current vol.

4-day log-return distribution is well approximated by the empirical bootstrap (s3) built from the d2 daily-return series (n=344).

Settlement price for Nov26 WTI contract tracks the front-month WTI series (d1) closely enough that d1's last value (90.59 on 2026-10-09) is a valid proxy for the starting point.

The d2/d3 return series are representative of the relevant contract's daily volatility regime as of Oct 2026.

No scheduled macro/geopolitical event on 2026-10-07 is known to the data provided (none flagged), so I treat the day as an ordinary trading day.

Settlement price for the Nov26 contract tracks the front-month/continuous series used in d1 closely enough that the 89.49 threshold maps to the -0.17% return threshold.

No major scheduled catalyst (EIA inventory, OPEC announcement) between 11:46 UTC and settlement is assumed absent from the data provided, so price action is treated as diffusion, not event-driven jump risk

d3's volume/OI collapse on 2026-10-06 (5382 vs ~335k prior days) reflects a contract-roll artifact in the Oct front-month series rather than a genuine liquidity vanish in WTI broadly

Daily log-return distribution (d2, s2) is a reasonable proxy for the Oct 6->Oct 7 settlement move

d4/d5 series (vol proxy, volume) are not WTI price series themselves and are only used as secondary context, not direct inputs to the probability calc.

Settlement reflects the same mechanism as the daily close/log-return series (d1/d2/d3), i.e., no basis divergence between the index used for d1 and the actual Kalshi settlement source.

No material scheduled catalyst (OPEC announcement, inventory data, geopolitical shock) between 11:46 UTC and settlement that would be known to shift the distribution materially; none is specified in the data.

d2/d3 return series are representative of the same underlying WTI contract dynamics relevant to the Nov-26 futures settling this question.

Threshold distance is small (0.167% below last close), so tail risk and distributional shape matter more than central tendency.

No material scheduled macro/geopolitical event (e.g., OPEC announcement, inventory shock) between 11:46 UTC and settlement is priced into the data provided; none disclosed in question context.

Daily log-returns are approximately stationary (confirmed by ADF, s5) and the relevant return distribution for Oct 7 is well-approximated by the trailing 40-day and 249-day empirical/bootstrap distributions.

Oct 6 close (89.64) is the most recent pre-settlement reference price for the Nov WTI contract.

No scheduled major supply shock (OPEC+ decision, EIA inventory surprise) between 11:46 UTC and settlement that is in my training data cutoff

Daily log-return distribution (d2, s2) is representative of the Oct 6→Oct 7 move despite the short 1-day horizon

Nov WTI contract settlement tracks the spot/futures series in d1 closely enough to use it as proxy

The settlement price moves roughly in line with the empirical distribution of daily returns (s2/s3) rather than jumping on a specific scheduled catalyst.

No material physical-market shock (OPEC+ decision, inventory surprise, geopolitical event) occurs between 10-06 and 10-07 that isn't already reflected in the return distribution.

Daily log/simple returns in d2 are representative of the return-generating process for the next settlement.

Last settlement (2026-10-06) close of 89.64 is the best proxy for the starting point for the Oct 7 settlement move.

No regime break occurs between the sampled historical period and the settlement date.

The Kalshi 1-minute settlement candle is not systematically biased vs the daily close series used in d1/s1/s2.

Last close 3.043 (10-05) represents pre-event price with no unlisted gap before 10-06.

Kalshi contract settlement price tracks the same underlying series as d1/d2 closely (basis risk not quantified here).

Daily return distribution (d2) is representative of the 1-2 day forward distribution (no regime change).

d1 last value (3.043) represents the most current available price feed, not stale.

No major scheduled EIA storage report or weather catalyst between now and settlement beyond what's embedded in historical return distribution (unverified, untested in data provided).

No major scheduled news (EIA storage report, weather shift) between 10/6 and 10/7 is priced into current data

Settlement price behaves similarly to the underlying daily close distribution scaled to a 2-day horizon (no regime shift/model risk from the specific 1-minute settlement mechanics)

d3 is a related but distinct return series (futures?) with positive autocorrelation, treated as secondary signal only

d2 represents daily log/pct returns of Henry Hub (sd=5.5%/day) used to project forward volatility

d1 represents Henry Hub daily close price series (last=3.043 on 2026-10-05), the most recent observed level ahead of settlement

d4 and d5 (storage/positioning data) are directionally informative but too noisy/infrequent (n=6, n=8) to materially shift the point estimate

No major scheduled catalyst (EIA storage report, weather shift) between Oct 6 and Oct 7 5pm that would be unusually large relative to typical daily moves — this is UNCERTAIN and not verified from the data provided

Daily log-returns are approximately i.i.d. for the purpose of scaling variance over 2 days despite known autocorrelation structure in commodities (mitigated here since autocorr_1≈0.016, near zero)

Settlement at 5pm EDT Oct 7 reflects the same underlying series as d1/d2 (Henry Hub or equivalent NG futures proxy), not a different contract with basis risk

Kalshi 1-minute candle settlement at 5PM EDT on Oct 7 will closely track the underlying NYMEX/physical front-month proxy represented in d1.

No major scheduled EIA storage report or weather-driven demand shock is assumed between 2026-10-06 and 2026-10-07 beyond what's embedded in recent realized volatility.

d6's persistent negative value (~-0.10 to -0.13) reflects a futures curve/basis spread metric (e.g., front-month minus deferred, consistent with contango) rather than the settlement price itself.

d2 represents daily log/pct returns of the same price series (mean ~0, sd ~2.49%), appropriate for estimating 2-day-ahead distribution.

d1 represents daily settlement/spot price series in USD/MMBtu ending at 3.043 on 2026-10-05, the most recent point-in-time price before the forecast horizon.

NFL home-field advantage base rate (~57-58% historical) is assumed to still hold in the 2026 season absent evidence of a specific injury/coaching shock

d1/d3/d4 are treated as binary win/loss indicators for some team over the last ~46-47 'games', but the entity (Cowboys? Buccaneers? a different proxy team?) is not specified in the data labels

d6/d7 are treated as market-implied win-probability series for DAL/TB respectively, but this is inferred from scale (0-1 bounded, mean near 0.4-0.5), not confirmed by metadata

d8 is interpreted as a market-implied point spread favoring Dallas by ~5-6 points, but the data has no explicit label confirming this — it could be a different quantity entirely (e.g., total, a different team's spread, or a derived index)

No explicit Kalshi order book depth, volume, or funding-rate data was provided, so true crowding/open-interest cannot be directly measured; I am inferring crowding from price stability and dispersion instead.

d3/d4 (n=352 each, noisy, with d4 collapsing to 0.005–0.115 on the last two 10/4 prints) likely reflect thinly-traded or stale order-book ticks (possibly bid/ask or a secondary prop) rather than a clean consensus probability — treated as low-reliability/noise.

d5/d6 (small integer series, trending 2→5 and 5→6 over Oct 1–4) are read as a widening point-spread / projected margin favoring Dallas.

d2 (n=118, mean≈0.20, tightly clustered at 0.195 through 10/3-10/4) is interpreted as the complementary (Tampa Bay) side of a two-sided binary market, implying Dallas ≈0.80–0.805 on the same system — this is an inference, not a labeled certainty.

d1 (n=9, mean≈0.69, last values 0.665–0.77 on 2026-09-29) represents sportsbook/market-implied win probability for Dallas, likely an early-week consensus.

No injury, roster, or weather information outside the supplied series is available as of 2026-10-05 02:39 UTC.

d3-d6 reflect Dallas's own game logs (home indicator, win indicator, margin) across a ~47-game window, used only to assess home-field effect, not opponent-specific adjustment for Tampa Bay.

d7 represents the point spread magnitude favoring Tampa Bay (away team) in recent updates, not a different line (e.g., total).

d1 is the Kalshi DAL-win contract price series for this specific game (KXNFLGAME-26OCT08TBDAL-DAL), not an unrelated market (e.g., season-long futures).

No injury, lineup, or line-movement information after 2026-10-04 (the last data point) is available; kickoff is Oct 9, so there are ~4-5 days of unobserved news (e.g., Friday/Saturday injury reports) that could move the line further.

d7/d8 represent injuries_out and injuries_questionable counts for one of the two teams (likely TB, given the market drifting toward DAL as these rose), but which team is not disambiguated in the provided handles.

d6 is the Kalshi-implied win probability specifically for the DAL contract (KXNFLGAME-26OCT08TBDAL-DAL) in the days leading into the Oct 9 kickoff.

d1/d3 correspond to Dallas's own win/margin series and d2/d4 to Tampa Bay's, based on series ordering and naming convention.

No play-by-play, QB status, or weather data were provided, so any 'fundamental' causal story is unverifiable from this data alone

d7/d8 are plausibly injury/roster-count style signals; their causal meaning is not stated and is uncertain

d1 is a binary historical outcome series (home-team win indicator) used to compute the n=51 base rate

d4 and d5 represent market-implied win probabilities for HOU and DAL respectively (not confirmed by metadata, inferred from sum≈1 and -0.94 correlation)

The as_of timestamp (2026-10-04 02:37 UTC) is close enough to kickoff that the flat last-six-observation price reflects the market's final settled view absent last-minute news

No data on injury reports, starting QB status, or weather was provided beyond the price series itself

d5-d8 are short, noisy historical binary indicators (recent game results or similar) with insufficient sample size (n~40) to update materially on their own

d1 and d3 represent Houston-side market-implied win probability (e.g., moneyline-derived or Kalshi contract mid-price) and d2/d4 the Dallas-side complement

No material information (injury, weather) occurred between the last data timestamp and kickoff that would move the line materially.

d3-d7 are binary win/loss and point-differential series from a reference set of prior games used to test ad hoc signals against the outcome; not clearly identified as current-season Texans-specific data.

d8 is a point-spread-like line (HOU favored by 3-4 points).

d1 and d2 are Kalshi contract prices for HOU and DAL respectively, sampled intraday leading into game time.

No team-specific partial-pooling model was fit in this session; I am not claiming to beat the market baseline, only reporting it.

d7/d8 (espn_spread, espn_total style series, n=6 each) are season-level weekly aggregates with very high variance and low n, too noisy to use as a standalone signal for this single game.

d5/d6 are injuries_out counts for the two teams (not labeled definitively), with d6 (mean 5, less volatile) corresponding to the team with consistently more players out.

d1/d2 represent the Kalshi-quoted win probabilities for HOU and DAL respectively, sampled repeatedly through the week with the last entries closest to kickoff.

Short 3-day horizon treated as too short for the weak weather-demand channel to realize even if it existed

No new fundamental shock (storage report, cold snap, pipeline outage) between as_of and settlement is assumed absent since none is in the data window

d1 is a reasonable proxy for the Kalshi settlement series (unverified basis risk between Henry Hub spot/futures and the specific 1-minute Kalshi print)

d3/d4/d5 are interpreted as open-interest / positioning style series showing a deepening negative trend (more short/bearish skew) into late September — directional interpretation is inferred, not confirmed by metadata

No major scheduled catalyst (EIA storage report, weather shift) between 10/02 and 10/05 is assumed absent from the data provided — this is an explicit gap, not a confirmed fact

Returns are approximately serially uncorrelated at the daily lag (autocorr_1≈-0.065 in s2), so a near-random-walk model for the 3-day horizon is defensible

Daily log-return distribution (d2, sd≈2.69%) is a reasonable proxy for near-term volatility despite the ADF test showing the price level series is non-stationary (s7)

Kalshi settlement at 5PM EDT 10/05 approximates the daily close price used in d1's history.

No major scheduled supply/demand shock (storage report, cold snap) is assumed between 10-02 and 10-05 beyond what's captured in recent price action and the HDD insight.

d2 is a daily return series usable for scaling to a 3-day horizon via sqrt(time) (iid approx), acknowledging this understates fat tails.

d1's last value (2.93 on 2026-10-02) is the relevant pre-horizon anchor price for the Kalshi settlement underlying.

3 trading/calendar days is sufficient for the autocorrelation-driven momentum to persist without a sharp reversal

No major weather or geopolitical shock between Oct 2 and Oct 5 is priced into the data provided

d5's steady drift toward more negative values (-0.114→-0.129 over 6 weeks, s6) reflects worsening storage/contango conditions rather than noise

d2 is the daily log-return series of d1

d1 is the Henry Hub / NatGas front-month settlement series used for Kalshi resolution

No major storage report or weather shock between now and settlement is priced into available data

Kalshi settlement tracks the underlying Henry Hub / proxy futures front-month price reasonably closely at the 5:00 PM EDT 1-min candle on 2026-10-05

d2 series represents daily log/pct returns of the same price series, sd≈9.87% is plausibly inflated by a few outlier days (skew 1.05, kurtosis 13.1, min -56.6%)

d1 series represents recent daily Henry Hub (or proxy) closing prices in USD/MMBtu, with last observation 2.93 on 2026-10-02

No scheduled macro/OPEC/EIA event between 10/3 and 10/5 is known to this analysis (as_of 2026-10-03 02:30 UTC) that would create a large deterministic jump

Daily return distribution (d2) is stationary enough over a 3-day horizon to use its sd for a rough vol estimate, even though s6 flags the underlying price level series as non-stationary (p=0.3)

d1's last value (92.83 on 10/2) is a reasonable proxy for the November WTI contract referenced in the Kalshi strike, despite possible spot/futures or contract-month basis mismatch

d3/d4/d5 series are proxies for implied volatility, inventory levels, and volume/open-interest respectively (labels not explicit, inferred from magnitude/units).

No major scheduled catalyst (OPEC+ meeting outcome, EIA inventory surprise, geopolitical shock) between Oct 2 and Oct 5 that is not already reflected in the data provided.

Kalshi settlement price tracks the CME WTI Nov'26 futures settlement closely with no material basis distortion.

Daily log-return distribution (d2) is stationary and the empirical bootstrap (s3) is a reasonable proxy for the next 3 trading days of WTI Nov'26 futures.

Kalshi settlement tracks the front/Nov26 futures contract closely with no idiosyncratic basis risk at settlement.

No major scheduled supply shock (OPEC+ meeting, EIA inventory surprise) is embedded in the data beyond what's already reflected in recent daily returns.

3-day bootstrap return distribution (s3) built from historical 3-day log-return windows is a reasonable proxy for the Oct2->Oct5 window despite non-stationarity in levels (s5).

Oct 2 close (92.83) is the best available point-in-time price anchor for the Nov26 WTI contract ahead of Oct 5 settlement.

Daily returns are approximately independent (autocorr_1=0.14, low) so 3-day variance scales roughly linearly

The Nov2026 WTI contract referenced in the Kalshi question tracks the d1 series without material basis divergence over 3 days

d3 (n=41, sd=2.77%, matches d1's daily % moves e.g. -4.54% on 9/30) is the corresponding daily return series for the same contract

d1 is the front-month WTI futures settlement price series (USD/Bbl), with last observation 92.83 on 2026-10-02

The Kalshi settlement price for the Nov WTI contract tracks the front-month/continuous series represented in d1 closely enough to use d1 as a proxy.

No scheduled macro/OPEC event between Oct 2 and Oct 5 is known to this analysis beyond what's reflected in recent price action (none supplied in data).

The 343-day return distribution in d2 is a reasonable proxy for the one-day-ahead return distribution despite some regime-shift risk from elevated recent realized volatility.

Oct 3-4, 2026 are a Saturday/Sunday, so only one trading session (Oct 5) separates the last observed close (Oct 2) from settlement.

d3 and d5 series are of uncertain provenance (not clearly WTI returns) and were downweighted due to high autocorrelation (0.637) suggesting a different, possibly smoothed or implied-vol series.

No regime change or scheduled macro/OPEC event occurs between Oct 2 and Oct 5 that is not already reflected in the return distribution.

3-day returns can be approximated by scaling daily sd by sqrt(3) despite d2's near-zero autocorrelation (0.015) suggesting weak-form efficiency.

d2 represents daily log/pct returns of the underlying WTI contract relevant to settlement.

The HDD/seasonal insight and COT regression are the only causal candidates offered and both fail robustness checks, so no fundamental catalyst is confirmed for the 3-day window.

The 5-day price decline in d1 is at least partially informative of near-term momentum, not pure noise, though this is not statistically tested here.

Henry Hub close behaves approximately as a driftless random walk at this horizon given ADF non-stationarity (s2) and no validated causal driver.

daily changes are approximately independent, which likely understates true autocorrelated risk

The Kalshi mid of 0.50 at as_of time is a reasonably liquid, two-sided market rather than a stale/illiquid quote

No major scheduled EIA storage report or weather-model flip occurs between Oct 2 and Oct 5 that is not already reflected in d5's trend

d5 reflects some bearish-trending fundamental or sentiment indicator relevant to weather/storage, not fully identified from the data alone

d1 is Henry Hub daily closing price level, d2 is the day-over-day dollar change in that price (confirmed by consistency between the two series)

The Oct 5 5pm EDT settlement will reflect the prevailing front-month/spot Henry Hub price with no major discontinuous news between now and then

d6 is a demand/supply proxy (e.g., LNG feedgas or weather-driven demand index) correlated with price per s5

d2 and d4 are daily (or related-frequency) return series on the same or correlated contract

d1 is the Henry Hub daily close/futures price series used for settlement

'over the horizon' is interpreted as the closing price on the Oct 5 settlement date

No major supply disruption (hurricane, pipeline outage) or demand shock occurs in the 3-day window that isn't already reflected in the historical return distribution

d2/s3 bootstrap distribution of 3-day returns is a reasonable proxy for the Oct 2→Oct 5 window despite no unique seasonal adjustment for early October

d1 series reflects the HENRY_HUB front-month/spot series used for settlement

No new scheduled macro/EIA/OPEC event between as_of and settlement is assumed, since none is given in the data.

d3 and d4 are unlabeled series (plausibly implied vol and volume/open-interest); without documentation I cannot verify what they measure, so I cannot validate any causal claim built on them.

Daily log-return volatility from d2 (sd≈3.23%) is a reasonable proxy for the distribution of the 1-day-ahead move even though d2's underlying asset/tenor is not explicitly labeled as WTI returns.

WTI.close on the resolution date is well-approximated by the last observed value in d1 (92.83 as of 2026-10-02), since as_of is only hours into that day.

d3 is open interest/volume for the Kalshi contract, d4/d5 are plausibly an implied-vol or weekly-return series for the underlying, used qualitatively only.

Remaining variance to close scales roughly with fraction of trading day remaining (~0.6-0.8x full-day variance).

d2's realized return series reflects daily log returns of the underlying WTI series in d1, confirming the 92.83 print is consistent (90.23->92.83 implies +2.88% log return, matching d2 last value).

d1's 2026-10-02 value (92.83) represents the live/spot WTI print at the as_of snapshot (02:30 UTC Oct 2), several hours before the official settlement/close used for resolution.

d4's high autocorrelation (0.859) describes a slow-moving volatility-level series, not evidence of return momentum (which is governed by d2/d3's near-zero autocorr).

Daily log/simple returns in d2/d3 are drawn from a regime similar to the current one (sd ≈2.88-3.3%), i.e., no structural break (war, OPEC emergency meeting) is imminently priced in beyond what's in the data.

The 2026-10-02 value of 92.83 in d1 is the most recent known close and the horizon's resolution close is the next observed WTI print within ~1 trading day.

No material scheduled macro/oil-supply event (OPEC meeting, EIA inventory shock) occurs between 02:30 UTC and settlement that would be larger than typical daily moves, since none is flagged in the data provided.

Required move to reach threshold from current level: ln(92.99/92.83) ≈ +0.172%.

d2/d3 are daily log-return series for WTI; d3 is a ~42-day recent-window subset, d2 is a longer ~274-day history.

d1's 2026-10-02 value (92.83) is a pre-close intraday/overnight print, not the final settlement; the resolution close is still to be determined later on Oct 2.

Market mid of 0.49 reflects a liquid, reasonably efficient options-like binary market

No major scheduled supply-shock event (OPEC+ meeting, EIA inventory surprise) is priced into the as_of window beyond what's in the return series

Returns in d2 are daily log returns computed from the same WTI series as d1

d1's last value (2026-10-02=92.83) is a pre-settlement/intraday print, not the final Oct 2 close that the contract settles on

No major scheduled supply/demand data releases (EIA inventory, OPEC action) are assumed between as_of and the Oct 2 close based on available data alone.

d4 is daily trading volume, and its sharp decline into the as_of date reflects reduced liquidity rather than a data artifact.

d3 is a term-structure/contango-related series (e.g., front-month vs. deferred spread) sampled weekly.

d2 represents daily log returns of WTI aligned with d1's dates.

d1's 2026-10-02 value of 92.83 is the most recent available print as of the 02:30 UTC as_of time, not yet the final settle.

The 'signal' tested in s3 and s5 is some fundamental or model-based predictor relevant to the home win hypothesis, though its exact definition is not stated

d7 and d8 are market-implied win-probability time series related to this contract or a reference set of similar contracts

d1-d6 represent some generic sample of team-games (possibly not limited to Saints/Falcons specifically), used as a proxy test of home-field and signal effects rather than a Saints-specific model

No line-moving news occurred between the last data timestamp and kickoff that is unobserved here.

d5/d6 represent injury or roster-absence counts, lower being better for the Saints.

d2/d3 are recent score-margin series for the two teams over their last 6 games.

d7 represents the point spread for this specific Oct 6 2026 game.

d1/d8 represent the Atlanta win-probability series for this matchup (Saints implied = 1 minus these values).

No single data handle directly encodes 'Saints win rate specifically when playing at home vs. Falcons,' so all inference here is an indirect composite, not a direct test of the resolution variable.

d7/d8 (n=8, very recent window) are short-horizon signals (e.g., weekly injury counts or similar) with wide bootstrap CIs (s7: [2.25,3.875], s8: [0.25,3.75]) that do not resolve directly to a win/loss signal and are too noisy to act on.

d5/d6 represent point-differential or margin series for the two teams; neither shows a significant difference (s3, s4 both p>0.25, CIs spanning zero).

d1 and d3 represent win/cover indicators for Saints and Falcons respectively (or vice versa) over the last ~46 games/weeks, though exact team attribution to each handle is not explicitly labeled in the provided data.

Preseason (August) games are included in the 46-game samples and add noise rather than signal for current team strength

d7 (injuries_out) reflects a recent reduction in missing players for one of the two teams, consistent with the market's upward move from a ~0.41 historical mean (d9/s7) to the current 0.56 quote

d3/d4 correspond to win-rate indicators for NO and ATL respectively (unconfirmed)

d1 and d2 correspond to NO and ATL point-margin series respectively (unconfirmed by explicit labels)

No injury report or lineup news beyond what is encoded in the line movement (d8) is available to me as of the as_of timestamp.

d1-d4 are unlabeled historical series whose relevance to THIS specific matchup (SF vs DEN) is unverified — I cannot confirm they are not for a different team, different market, or even a different sport subset.

d5 represents an implied win-probability time series that is informative about this game as of 2026-09-30/10-01, not a different market or team.

d8 represents the actual closing/near-closing spread line for this specific SF-DEN game, with -3 being the posted line referenced in the question.

No access to actual injury report details; the large line move is inferred to reflect material news not explicitly described in the data.

d5/d6/d7 are margin-of-victory distributions for league-wide, SF, and Denver (or opponent) games respectively, used only as rough context, not direct forecast inputs.

d3 and d4 are devigged moneyline-implied win probabilities for SF and Denver respectively (sum to ~1.0), not ATS probabilities.

d1 represents the historical/closing spread line for this game with SF as favorite, moving from -7.5 to -3.

The binary series d3/d4/d5 encode some situational signal tested in s3/s4/s7; I defer to the reported statistics rather than assuming their exact content.

d6/d7 are market-implied win probabilities (moneyline-derived) for SF and Denver respectively, not direct cover probabilities.

d8 represents the closing spread line for SF in this specific matchup over time, with -3 being the operative current number referenced in the question.

d1 represents SF's historical scoring margin (point differential) across a relevant game sample, used as a proxy for the distribution of plausible outcomes in this game.

Game has not yet been played as of as_of timestamp (2026-10-01 02:30 UTC); kickoff is 2026-10-04.

No injury data (d6, d7) could be definitively attributed to SF vs. Denver, so I treat the injury trend (declining counts into game day) as inconclusive for directionality.

d1 is SF's own margin series and d2 is either Denver's or a league-wide comparison series; sample sizes (n=41, n=42) are too small and high-variance (sd~14.7-14.85) to support strong form inference.

d4/d5 represent complementary Kalshi win probabilities for SF and DEN respectively (0.575+0.425 approx 1.0), not cover probabilities.

d3's last two entries (-7.5, -3) represent the spread trajectory for this specific SF-DEN game across the week, with -3 as the closing/game-day number.

The 178-obs historical return distribution (s1) is a reasonable proxy for tomorrow's conditional distribution despite regime mixing (sd/mean computed over a window spanning $59-$113 prices).

No major scheduled event (OPEC+ decision, EIA inventory, geopolitical shock) between the as_of time and Oct 1 close is known to me; if one exists it would dominate this analysis.

d2's last five values reproduce d1's realized daily percentage changes almost exactly, so d2 is (or is derived from) WTI's own return series, not an independent predictor.

d1 close series and the Kalshi WTI.close settlement reference the same benchmark.

No new macro/geopolitical catalyst between 11:30 UTC and the Oct 1 close is assumed beyond what's already reflected in today's move.

The Kalshi mid-price of 0.49 was quoted at 11:30 UTC and may not have fully updated to reflect the -4.4% intraday move captured in d2's last value.

d3's flag=1 on 2026-09-30 identifies today as a 'similar catalyst' event day matching the event-study sample used in s3.

The d1 series last value (89.35 on 2026-09-30) is the most recent official WTI close and is what the Oct 1 settlement will most likely anchor near.

No access to intraday news after 2026-09-30 11:30 UTC that may already be moving the market (e.g., the -4.44% print on Sep30 itself may reflect information not fully captured in a static historical distribution).

The Oct 1 2026 close is a single 1-day-ahead draw from a return distribution similar in shape to the trailing ~620-day sample (no regime change assumed beyond what's in the data).

d5 is a proxy for weekly realized/implied volatility (values 0.07-0.14 range, rising into late Sept).

d2/d3 represent WTI daily log or simple returns aligned to d1 closing price series (dates roughly match with 1-day lag in labeling).

Kalshi mid-price of 0.49 reflects genuine two-sided market pricing, not a stale/illiquid quote.

No scheduled macro/OPEC event between as_of and Oct 1 close is known to the model that would shift the distribution (none provided in data).

The empirical daily log-return distribution (d2/d3, n=480) is a reasonably stationary proxy for the one-day-ahead return distribution, despite recent elevated volatility.

The d1 series close of 89.35 dated 2026-09-30 is the last observed WTI close prior to the Oct 1 settlement in question.

No major scheduled catalyst (OPEC+ meeting, EIA inventory shock, geopolitical event) between 9/30 11:30 UTC and Oct 1 close is embedded in the data provided.

The 'signal' in d3/d5 (triggered =1 on 2026-09-30, coincident with the -4.54% return) is a volatility/shock indicator being tested against next-day outcomes in s2/s3.

d2's daily log/simple return series is representative of the return-generating process for the next 1-day horizon (no regime break).

d1's last value (2026-09-30=89.35) is the most recent observed WTI price/level as of the as_of timestamp (11:30 UTC 9/30), prior to the Oct 1 close resolution.

d3 (volume/open interest) spike on 9/28 is noted but not decisively interpreted as directional signal given lack of price-volume correlation test.

No material scheduled catalyst (e.g., OPEC+ meeting, EIA report) between 9/30 11:30 UTC and Oct 1 close is known to me beyond what's in the data.

The 21-day and 502-day return samples are representative of current volatility regime (no major regime break since 9/30).

WTI.close for the Oct 1 resolution is a single new trading-day close, not an intraday high or futures-settlement quirk.

d3 and d4 are auxiliary series (e.g., a rate/vol series and a volume-like series) whose correlation with price (s4-s6) is being offered as a causal/predictive story worth stress-testing.

The remaining hours between 11:30 UTC and the Sep 30 settlement retain meaningful but likely less-than-full-day variance, since a large chunk of the day's move has already occurred.

d2's last value (-0.0454) is the log return realized so far today (ln(89.35/93.5) ≈ -0.0454), confirming a sharp overnight/morning decline already priced in.

d1's 2026-09-30 value (89.35) is a live intraday quote at/near the as_of timestamp, not yet the settlement close.

No unscheduled macro catalyst (EIA data, OPEC announcement, geopolitical shock) occurs between 11:30 UTC and settlement that would materially skew the distribution today specifically.

Log returns from this point to end-of-day settlement are approximately normally distributed with parameters similar to the trailing 82-day sample (s2).

The 89.35 print in d1 for 2026-09-30 is a genuine live/near-live quote as of 11:30 UTC, not a stale or erroneous data point.

The Kalshi contract resolves on the same WTI benchmark/timestamp convention as the data series provided.

No unmodeled scheduled catalyst (EIA inventory report, OPEC statement, geopolitical shock) between 11:30 UTC and close is assumed beyond what's already priced into the -4.4% move.

Daily log-return distribution (d2/s2) is a reasonable proxy for the magnitude of remaining intraday moves, even though roughly half the trading session has already elapsed by 11:30 UTC.

The d1/d3 'last' value dated 2026-09-30 (89.35) is a live/interim quote at the 11:30 UTC as_of time, not yet the final settlement close (WTI settles ~14:30 ET / 18:30 UTC).

No scheduled macro/OPEC event catalysts are assumed beyond what's embedded in recent realized volatility (none provided in data).

d2 is the daily return series aligned with d1 levels; its moments approximate the unconditional daily move distribution.

Daily settlement occurs later in the session (~18:30 UTC CME close), so roughly half the day's typical volatility window remains at as_of time.

d1 2026-09-30 value (89.35) is the current/intraday WTI price as of the 11:30 UTC snapshot, not yet the final settlement close for the day.

Returns are approximately normally distributed intraday (ignoring the mild positive skew/kurtosis seen in s2).

No major scheduled catalyst (e.g., EIA report, OPEC announcement) between 11:30 UTC and settlement is assumed absent from the data; none is provided.

Daily log-return volatility (sd=3.24% from d2) is representative of near-term volatility and scales roughly with sqrt(time remaining).

Official WTI settlement ('close') occurs ~2:30pm ET (18:30 UTC) during EDT, i.e. ~7 hours after the as_of timestamp.

d1's 2026-09-30 value (89.35) is today's most recent observed/intraday WTI price as of 11:30 UTC, not yet the final settlement.

d4 (volume) at 16,010 vs mean 220,200 indicates unusually thin trading around the as_of snapshot, raising the chance of choppy, low-conviction price action rather than a decisive rally.

d3 (contango/basis measure) rising to a 12-week high (0.08833) reflects a genuine supply-side signal (steepening contango typically implies near-term oversupply pressure), not noise.

WTI futures settlement for the referenced contract occurs in the afternoon (~18:30-19:30 UTC), leaving a meaningful fraction of the trading session after the as_of snapshot.

d2 is the day-over-day price change series in dollar terms (last entry -4.15 matches the drop from 93.50 to 89.35), used as a proxy for full-session volatility.

d1's last value (89.35, dated 2026-09-30) is an intraday/pre-close quote observed at or before the 11:30 UTC as_of time, not yet the final settlement.

d4 and d5 are not usable as causal levers given their weak/unstable statistical relationship to price (s4-s7).

No scheduled macro/OPEC/EIA event between 2026-09-29 11:30 UTC and settlement on 2026-09-30 is known to me; if one exists, market's 0.52 may be informed and my estimate is wrong.

Return distribution (d2/d3, s2) is approximately stationary over the relevant 1-day horizon (justified weakly by ADF test s3 on levels of returns, not on tail behavior).

The 2026-09-29 value of 93.5 in d1 is the settled/last traded price used as the reference for the 1-day-ahead question, not a stale or intraday snapshot.

Low d4 volume reflects thin market participation rather than a deliberate, well-informed price

No unscheduled macro/OPEC catalyst occurs before the 9/30 close that would be unusually large relative to the trailing 82-day return distribution

Daily log returns are approximately normally distributed at the 1-day horizon (supported by s2's low skew/kurtosis)

d1's last value (93.50, 9/29) is a reasonable proxy for the settlement reference used by the Kalshi contract

The as_of market quote (0.52) is a genuine mid-market price and not stale or reflecting a different strike/contract structure than described.

No major scheduled catalyst (OPEC decision, large geopolitical shock, EIA data surprise) occurs between as_of (Sep 29, 11:30 UTC) and settlement that would be unusually large relative to the historical distribution.

The 502-day historical return/price-change distributions (d2, d3, s1, s3) are representative of near-term volatility regime (no material regime shift into Sep 30).

d1's last value (93.50 on 2026-09-29) is the same reference price the Kalshi contract will settle against on 2026-09-30.

Series is treated as return-stationary per ADF (s4), supporting use of the unconditional return distribution rather than a trending/non-stationary model.

The bootstrap distribution (s3) and normal approximation using s2 moments are both reasonable approximations for tail risk despite the documented negative skew and excess kurtosis.

Daily log-return distribution (d2, n=171) is a valid generative model for the Sep 29->Sep 30 return, i.e., no unusual regime shift or scheduled shock (OPEC+ meeting, EIA report, quarter-end flows) is expected to alter volatility materially.

The last observed WTI value (93.5 on 2026-09-29) is a reliable proxy for the price level at the start of the 1-day resolution window.

No overnight/weekend gap risk distorts the 1-day resolution (Sep 29->Sep 30 is a normal consecutive trading day).

d3-d6 (degree-day/storm-index style series) have only indirect, weak linkage to WTI (more relevant to nat gas/refined products) and are not treated as primary drivers of a 1-day crude price move.

d2 is the corresponding daily log/simple return series (n=274) used to estimate one-day move distribution.

d1 represents actual WTI daily closing prices, with 2026-09-29=93.5 being the most recent price ahead of the Sep 30 resolution.

The Kalshi contract settles on the official WTI close for Sep 30, 2026, consistent with the d1/d3 series definition, not an intraday low/high.

No unscheduled shock (geopolitical event, surprise OPEC action, large EIA inventory surprise) occurs between the 9/29 close and 9/30 close beyond what is embedded in the historical unconditional return distribution.

d2 represents daily returns of the same series (values track d1 level changes in sign/magnitude, e.g. -6.4% on 9/22 coincides with the low d1 print of 89.84).

d1/d3 last value (93.50 on 2026-09-29) represents the current WTI front-month close used as the base for the 1-day-ahead resolution.

Return distribution in d2/d3 is a reasonable proxy for remaining intraday volatility, adjusted downward for partial-day vs full-day horizon

The 90.49 strike references the same WTI series as d1 (no cross-source mismatch between Kalshi settlement source and d1 feed)

NYMEX WTI front-month typically settles ~18:30 UTC, i.e. ~7 hours after the as_of timestamp, so 'close' for today is not yet fixed

d1's 2026-09-29 print of 93.50 is a genuine point-in-time observation available at 11:30 UTC, not a post-hoc backfilled settlement value inserted with look-ahead bias

The Kalshi settlement reference price is comparable to the WTI series represented by d1.

d5's daily fluctuations (1.1e4 to 4.4e5) represent Kalshi contract volume/open interest for this specific strike, indicating a thin, potentially inefficient market.

Settlement occurs several hours after 11:30 UTC (partial trading day remaining), so relevant variance is a fraction of the full daily variance (sqrt-time scaling).

d2 (n=171, mean~0.0033, sd=0.0407) represents daily log returns of WTI and is a valid proxy for near-term realized volatility.

d1's last value (93.5 on 2026-09-29) is a reasonably current WTI price near the 11:30 UTC as_of timestamp, not a stale or mismatched-session print.

No scheduled macro/OPEC catalyst between 11:30 UTC and settlement is assumed absent evidence to the contrary (none in the data provided).

d2/d3/d5 log-return series are representative of the relevant volatility regime (they include the most recent turbulent week, so are not understating current vol).

NYMEX WTI daily settlement occurs roughly 14:30 UTC (~2:30pm ET); as_of 11:30 UTC leaves a partial trading session, so remaining-session volatility is a fraction of full-day close-to-close volatility.

The 2026-09-29 value in d1 (93.5) is an intraday/available print at or near the as_of time (11:30 UTC), not yet the final settlement close.

No major scheduled macro/geopolitical event between 11:30 UTC and settlement is assumed absent from the data; this is not explicitly tested.

Daily log-return distribution (s2/s3) is a reasonable proxy for the remaining intraday volatility between 11:30 UTC and settlement, even though it slightly overstates risk since part of the trading day has already passed.

The Kalshi settlement price for KXWTI-26SEP2914-T90.49 tracks the same WTI series represented in d1/d2/d3 without material basis risk.

d1's last value (93.50, dated 2026-09-29) is a legitimate, current, executable WTI price observed at or near the as_of time (11:30 UTC).

Weather/degree-day data (d3, d4, d5, s3, s4) are not materially informative for a 1-day WTI price move at this horizon — no significant, decision-relevant correlation was found (s4 p=0.272, n=4).

d2's return series represents daily WTI log/pct returns and is a reasonable (if fat-tailed) proxy for intraday volatility over the remaining hours.

The settlement/close referenced in the resolution rule occurs later the same day, giving a partial (not full) remaining trading session for the price to move.

d1's last value (93.50, dated 2026-09-29) reflects the current/live WTI quote at or near the as_of timestamp (11:30 UTC), not a stale or mismatched-contract print.

Resolution is based on WTI futures settlement price (WTI.close), consistent with the underlying series in d1.

Daily log-return distribution (d2/s2) is a reasonable proxy for the remaining volatility budget over the horizon, even though roughly half the trading day may have already elapsed by 11:30 UTC, which would make actual realized vol lower than the full-day figure used.

The as_of timestamp (2026-09-29 11:30 UTC) sits within the settlement day, so the last WTI print (93.50) is either today's live price or yesterday's close carried forward — in either case it represents the starting point for the remaining 1-day horizon.

d4/d5 (volume/OI-like series) are not shown to have any tested causal link to next-day WTI direction in the provided stats

The 2026-09-29=93.5 entry in d1 is a same-day quote near the as_of timestamp (02:30 UTC), not yet the final settlement close that the question resolves on

d2/d3 are daily log-returns of WTI and a closely related series (likely Brent or a lagged WTI feed) — their near-identical descriptive stats (mean, sd, last values) suggest d3 may just be a 1-day-lagged copy of d2, i.e. potential leakage/duplication rather than an independent predictor

d1 is the WTI price level series (daily close), currently non-stationary per ADF (s3)

Kalshi contract KXWTI-26SEP2914-T93.49 settles on the NYMEX WTI front-month official close for trade date 2026-09-29, several hours after the as_of snapshot.

d3 is a basis/spread proxy (e.g., futures curve backwardation measure); d4 is a volume or open-interest series; d5 is an inventory-like series (e.g., EIA stocks) — exact identities are inferred from scale, not confirmed metadata.

d2 is the daily log-return series for the same WTI series in d1.

The d1 series 'WTI' last value (93.5 on 2026-09-29) is an intraday/pre-close quote captured near the 02:30 UTC as_of time, not the final settlement price used for resolution.

No major scheduled catalyst (OPEC+ meeting, EIA inventory shock, geopolitical event) is assumed between 02:30 UTC and settlement beyond what's already embedded in recent volatility.

The 1-day horizon means the resolving 'close' is the same-day (Sep 29) NYMEX settlement, only hours away from the anchor price -- i.e., this is effectively an at-the-money strike bet.

d2 is the daily log-return (or simple return) series for WTI used to characterize one-day move distribution.

The d1 2026-09-29 value (93.50) is the most recent intraday/settlement print available at the 02:30 UTC as_of time and is treated as the anchor from which the final close moves.

No transaction costs or execution delay considered since this is a probability estimate, not a trading backtest.

d3, d4, d5 are exogenous/event-type series (e.g., inventory surprise, scheduled-event flags) not causally tested against next-day returns in this analysis; they are treated as unconfirmed signals.

The unconditional 516-obs daily return distribution (s2) is a reasonable proxy for the distribution of the remaining move to the day's close, despite not being a true 'remaining hours' distribution.

The 2026-09-29 print of 93.50 in d1 is a valid point-in-time price near market open/Asian session, prior to U.S. settlement.

No major scheduled macro/EIA/OPEC event is assumed between 02:30 UTC and settlement that would independently be known to invalidate a random-walk assumption (untested, no explicit data on this).

Historical daily log-return distribution (d2/s2) is a reasonable proxy for same-day residual volatility between the as_of snapshot and settlement, though the true remaining-time vol is smaller than a full 24h since part of the day may have already elapsed.

The 1-day horizon means resolution occurs at the Sep 29 NYMEX close/settlement, several hours after the as_of snapshot.

d1's last value (2026-09-29=93.5) is a point-in-time snapshot of the current/last-traded WTI price near the as_of timestamp (02:30 UTC), not yet the final settlement close for the day.

Implied vol proxy d3 rising to 0.0883 (highest in the 8-week series) signals elevated near-term uncertainty but is treated as within-sample, not a regime break.

No major scheduled macro/OPEC/EIA event is assumed between as_of and the Sep 29 close that would produce an outsized one-day move beyond what's captured in the historical return distribution.

Daily log-return distribution from d2 (n=171) is representative of the current regime's volatility and drift.

The 2026-09-29 value in d1 (93.50) is an intraday/pre-close quote at the 02:30 UTC as_of time, not the final settlement — the resolution close is still to be determined over the remaining trading session.

n=46-48 observations likely correspond to a small multi-season game log for one team, not a large enough sample to support a stable regression coefficient

d2, d3, d5, d7 are unlabeled numeric/binary series (point differentials, opponent strength, or similar) whose exact construction and relation to the outcome variable is unverified

d1 is plausibly a CLE win/loss indicator (binary, mean 0.30) and d4 plausibly a home-win indicator (binary, mean 0.52), but data handles carry no semantic labels in the provided package, so this is inference, not observation

d6 is the Kalshi market price series itself for this contract (values 0.37-0.515 match the stated market description), making s8's bootstrap CI a statement about market price stability, not an independent estimate of true win probability

No line-movement or volume/open-interest data was provided, so crowding must be inferred from price stability alone

d3-d6 are auxiliary game-level indicators (spread-like and binary outcome flags) whose exact construction is not fully specified, limiting interpretability

d2 represents an alternative probability signal (e.g., a different book, model, or public-money proxy) rather than the same contract

d1 represents the tracked Kalshi mid-price series for CLE win contract over recent months

No new information post as_of (injuries, weather, lineup changes) is available beyond what is encoded in d6's market drift

d4/d5 (n=48) pertain to a different entity (e.g., opponent Steelers or a different signal) and are not directly load-bearing for CLE's win probability absent a labeled linkage

d6 is the time series of the market-implied probability itself (mean 0.4282, matches quoted 0.42)

d3 represents point differential associated with the is_home regression in s3/s7

d1 represents CLE win/loss indicator across a rolling sample of n=46 games (mix of home/away)

No player-level injury detail (positions) available, so injury impact is a count proxy only, per role guidance

d6 = Kalshi CLE win-probability tick series for this contract, d7/d8 = injury counts (out/questionable) for the two teams, likely CLE=1 out, PIT=2 out as of last snapshot

d4/d5 = PIT win indicator / margin series (n=45)

d3 = CLE is_home indicator (~49% home, consistent with schedule)

d1 = CLE win indicator by game (n=43, chronological), d2 = CLE scoring margin

No test provided controls for opponent strength, rest days, or injury status — all first-order NFL outcome drivers — so any signal found in d1-d6 could easily be a proxy for schedule/opponent quality rather than a causal driver of this specific matchup.

The market series d7 (n=275, nearly constant at ~0.475-0.489, autocorr=0.974) is treated as the operative external prior since it aggregates information (injuries, roster, coaching, weather) not present in d1-d6.

d1-d6 are proxy indicators for team/game-level performance metrics (win indicators, point differentials) whose exact construction and team assignment (TB vs. MIN, home vs. away) is not documented in the handles provided, which itself is a labeling-ambiguity risk.

No injury report, weather, or line-movement data beyond these series was available

d3-d5 are binary outcome indicators (win/loss or cover) with means near 0.5-0.63, too noisy to interpret confidently without more metadata

d6 is TB's recent point differential (game-level), with negative recent values indicating recent poor performance/margin

d2 is a distinct, more volatile market/signal (possibly a spread-implied or in-season adjusted probability) whose late spike to 0.815 on 2026-09-20 reflects new information not yet fully absorbed into d1

d1 tracks the market-implied win probability time series for TB (or a closely related book) given its tight range and proximity to the stated Kalshi mid of 0.47

'is_home' regression in s3 uses the same 46-game panel as d1/d3, testing whether home games produce better point differential/win outcome for TB

d6 is the time series of the market-implied probability itself (275 snapshots), currently converged near 0.475

d3/d4 are score differentials, d7/d8 points scored/allowed for TB

d2 is a comparison series (possibly Vikings' win indicator or a different signal) not directly used given ambiguity

d1 represents TB's win indicator (1=win,0=loss) across its last 46 games (mix of home/away, includes playoffs/preseason markers)

No knowledge of the identities/positions of injured players beyond the count; cannot assess replacement quality directly.

Injury counts (3 out for TB, 2 out for MIN) are a rough proxy for missing talent, not weighted by position importance.

tb_kalshi series showing 0.475 repeated across multiple 2026-09-27 timestamps suggests the line has settled, not still reacting to news intraday.

Kalshi mid at as_of time (0.475) reflects the most recent information, including any injury news already priced in.

Kalshi mid of 0.50 reflects genuine two-sided order flow, not thin/stale quotes

No new macro/weather shock occurs between 9/26 and 9/28 that isn't already reflected in current price/positioning data

d2-d8 are auxiliary series (returns/positioning/weather) whose exact definitions are not fully specified in the handles, which itself limits how much causal weight they can bear

d1 represents the Henry Hub daily close series used for resolution (last obs 2026-09-25 = 3.237)

Kalshi mid-price is a genuine tradeable quote, not stale/wide due to illiquidity, though evidence suggests it may be exactly that.

d4 represents volume/open interest for the relevant contract or a proxy for market participation.

d2 series represents daily returns of the underlying gas price; d1 represents the underlying daily close level.

Daily log-return distribution is approximately stationary over the very short 2-day horizon (no regime break, e.g., hurricane/storage shock).

Last observed Henry Hub close (2026-09-25) = 3.237, already 0.68% above the 3.215 strike.

d1 series (last close 3.237 on 9/25) is the correct proxy for Henry Hub level used in resolution.

No major supply shock, pipeline outage, or weather-driven demand surprise occurs in the 48-hour window that is not already reflected in recent price action.

The 2-day horizon (9/26 to 9/28) spans essentially 2 trading/settlement observations.

Henry Hub daily closes behave approximately as geometric random walk with drift matching recent 342-day log-return sample (d2/d6).

No futures curve (contango/backwardation) data was available in this data pull, which limits my ability to assess whether current spot strength is priced into the forward curve

d5's stable negative series (~-0.11 to -0.12) is some storage or basis anomaly metric; interpretation is uncertain so I discount it heavily

s3 Monte Carlo bootstrap (10,000 sims, 2-day horizon) using the return distribution in s2/d2 is a reasonable proxy for the 2-day price move needed for this question

d2/d6/s2/s6 represent daily log or simple returns of Henry Hub spot/futures

d1 represents recent daily Henry Hub close levels (last obs 2026-09-25 = 3.237)

The autocorrelation structure in s1 (0.92) reflects genuine persistence and not primarily a data artifact of infrequent sampling.

No unannounced fundamental shock (storage report surprise, hurricane, pipeline outage) occurs between 9/25 and 9/28 that isn't already priced in.

d2 represents Henry Hub (or a closely tracking series') daily log/pct returns, not a derivative or different instrument.

The bootstrap in s3 is drawn from the same return distribution (d2) and is a reasonable proxy for the 3-day forward return distribution from the current close of 3.237

d5 represents volume or open-interest-change proxy, declining sharply into the last 3 sessions

d3/d4 represent positioning or curve-structure series (e.g., net spec positioning, basis) sampled weekly, not directly convertible to a probability but useful as crowding proxies

d2 represents daily/log returns series feeding the bootstrap in s3

d1 represents Henry Hub daily close price series ending 2026-09-25 at 3.237

No major scheduled weather/storage-report surprise between 9/25 and 9/28 is priced differently than history implies.

d3 (a series positively correlated with price, s5 corr=0.91) is a demand-side proxy (e.g., LNG feedgas nominations) rather than storage, given it rises together with price.

d2 is the daily return series for the same Henry Hub series used to bootstrap 3-day forward moves in s4.

"close level over the horizon" is interpreted as the settlement price at/near the Sep 28 5pm EDT resolution timestamp, not a max-over-window condition.

The d1 series represents Henry Hub daily settlement/spot closes and the last printed value (2026-09-25=3.237) is a real settle, not a stale intraday quote.

No major scheduled event (EIA storage report, hurricane, cold snap) between 9/25 and 9/28 is factored in beyond what's already reflected in d6/d7's recent trend.

3-day volatility scales roughly as sqrt(3) times the daily sd from d2, ignoring any anomalous seasonal mean-reversion near contract settlement.

d6 and d7 are physical-market series (storage flow and a demand/weather-linked index respectively) whose recent trends are directionally informative for near-term price even though no formal regression/backtest was run linking them to forward HENRY_HUB.close.

d2 represents daily log/percent returns of HENRY_HUB.close (confirmed by matching the 9/22 +10.85% value to the observed 3.161 level jump from 2.836 in d1).

The market's 0.54 mid already reflects most public information as of 2026-09-19; my job is to find what it's missing, and the tests supplied don't clear that bar.

No committee member has yet shown a differenced, regime-stable, out-of-sample relationship between any driver series and WTI closes; until they do, I treat t3/t4 as unconfirmed.

d2, d3, d4, d6 are return/log-return series (small sd 0.02-0.05) and d7 is a binary event flag (mean 0.051, ~5% of days).

d5 is a trending, likely non-stationary level series (inventory, open interest, or a day-count-to-expiry proxy) rather than a stationary return series, given its scale (118.6-423.3) and monotonic recent run-up.

i.i.d. normal returns with unconditional sd; ignores volatility clustering after the large recent move

The resolution rule refers specifically to the Sep 21 close, not any intraday touch of 95.99 during the horizon

d7/d8 are binary event indicators (e.g., storm or cold-snap flags) used in the conditional-probability/event-study tests

d2/d3/d4 are degree-day or weather-index style series (means ~35-37) used to test a weather->oil-return channel

The 2d horizon (Sep 19 -> Sep 21, a weekend) corresponds to approximately one trading-day return from Friday close to Monday close

d5 is the corresponding daily return series for the same underlying (mean+sd consistent with WTI daily vol)

d6 is the WTI price level series and its last value (2026-09-18=96.73) is the most recent close before as_of

d3, d4, d5 represent correlated cross-asset factors (e.g., dollar index, equities, rates) based on their correlation strength with d2 (s4 corr=0.57, s5 corr=0.40, s6 corr=0.75), but their exact identity is not specified, so I cannot use them for a directional call beyond noting typical macro-oil linkages.

No major scheduled macro/OPEC event is known to occur in the 2026-09-19 to 2026-09-21 window based on the provided data.

The 95.99 strike refers to WTI closing level on 2026-09-21, consistent with d1's daily closing series.

Daily log returns are approximately independent (supported by autocorr_1=0.0118 in s2), so a 2-day random walk with normal-approximated returns is a reasonable first-pass model.

d3/d4/d5 are treated as auxiliary covariates (e.g., volume/OI/related-commodity proxies) whose correlations with d1 are noted but not used to shift the point estimate, per the explicit inflation warnings in t5/t7.

No transaction costs, liquidity, or bid-ask spread effects are modeled; this is a probability judgment, not a trade recommendation.

The Kalshi mid-price of 0.54 was set after the 2026-09-18 close and therefore already reflects any information in the last observed d1 value.

d2 is treated as the daily return series computed from the price d1 proxies (or a closely related quantity); its magnitude (sd=0.033, one recent value -0.072) is consistent with, but not proven identical to, the ~7.8% single-day move visible in d1's last two points.

d1 is treated as the closest available proxy for the WTI closing price level referenced in the resolution rule; the exact unit/scale mapping between d1's values and the $95.99 strike is not confirmed by the data provided, which is a material source of uncertainty.

The reported 'mid' of 0.54 is a reasonably tight, liquid quote and not itself distorted by a wide bid-ask spread typical of a thinly-traded binary strike.

No material new fundamental catalyst (OPEC action, geopolitical shock, inventory surprise) arrives between 2026-09-19 and 2026-09-21 that isn't already reflected in the 9/18 price action.

Daily log returns are the right unit to compound over the 2-day horizon and independence (near-zero autocorr_1=0.0149, t2) is close enough to true for a first-pass Normal approximation.

Kalshi's KXWTI-26SEP2114-T95.99 settles on a single closing-price observation on 2026-09-21 rather than a path-dependent 'stayed above at all times' condition (unconfirmed from the prompt's resolution text).

2-day horizon return distribution approximated as sum of i.i.d. daily returns (mean and variance additive); no explicit weekend/settlement adjustment

No EIA inventory, Cushing storage, or futures curve (contango/backwardation) data was provided in this evidence set — a material blind spot for a commodities-balance argument

d4 and d5 are correlated but distinct series (possibly Brent, gasoline crack, or equity-linked energy proxy) that I could not physically identify from data alone

d3 is a longer/related return series (possibly WTI at higher frequency or a longer lookback) used to estimate baseline volatility

d1 = WTI daily close level series; d2 = WTI daily log returns (confirmed by matching 9/18 return of -0.05083 to ln(96.73/101.9))