anomaly-atlas
Honesty doctrine. Every candidate anomaly is an artifact until proven otherwise; in-sample results are never findings; past statistical regularity does not imply future returns. This is research on statistical properties of market data — not investment advice, not a trading system.

Research / research/notes/timeseries_methodology.md

Phase 1 notes — time series methodology

reviewed

Phase 1 notes — time-series methodology · created Tue Aug 11 2026 20:00:00 GMT-0400 (heure avancée de l’Est) · Simon-Pierre Boucher

Time-series methodology (§4.4)#

Phase 1 literature notes. Citations verified via OpenAlex, accessed 2026-08-12.

1. Variance ratios & long memory#

  • Lo & MacKinlay (1988) — the VR test itself (see mean-reversion notes). Implementation lesson learned in OUR code: the §8.1 synthetic gate caught a double-division-by-q bug in our first VR implementation — the estimator read ~1/q on a pure random walk. Estimator subtleties are real risks, not textbook trivia.
  • Lo, A. W. (1991). Long-Term Memory in Stock Market Prices. Econometrica 59(5), 1279–1313. https://doi.org/10.2307/2938368 — modified R/S statistic robust to short-range dependence; classic R/S (and naive Hurst estimation) mistakes short memory + heteroskedasticity for long memory. Any Hurst-based Q1 claim must use Lo's correction and a bounce-aware null.

2. Granger causality caveats#

  • Granger, C. W. J. (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Econometrica 37(3), 424–438. https://doi.org/10.2307/1912791 — predictive content, not causation. For Q2 at 1min: Granger "causality" from fresh to stale series is guaranteed by non-synchronicity (expB measured it); only both-fresh subsamples and staleness-matched nulls make the test meaningful.

3. Bootstrap for dependent data#

  • Künsch, H. R. (1989). The Jackknife and the Bootstrap for General Stationary Observations. Annals of Statistics 17(3), 1217–1241. https://doi.org/10.1214/aos/1176347265 — moving-block bootstrap (our stats/bootstrap.py).
  • Politis, D. N. & Romano, J. P. (1994). The Stationary Bootstrap. JASA 89(428), 1303–1313. https://doi.org/10.1080/01621459.1994.10476870 — geometric random block lengths → stationary resamples; the resampling engine inside White's Reality Check. To implement for expF.

4. Splits, walk-forward, CPCV#

  • Bailey, Borwein, López de Prado & Zhu (2016). The probability of backtest overfitting. Journal of Computational Finance 20(4), 39–69. https://doi.org/10.21314/jcf.2016.322 — CSCV/PBO: combinatorial splits measure how often the in-sample winner underperforms out-of-sample. Candidate for expH; must be combined with purging (no leakage across split boundaries — overlapping bars/labels).
  • Charter constraint: the final holdout is touched ONCE (§8.2) — CPCV operates strictly inside the train/validation region.

5. Structural breaks & regimes#

  • Bai, J. & Perron, P. (1998). Estimating and Testing Linear Models with Multiple Structural Changes. Econometrica 66(1), 47–78. https://doi.org/10.2307/2998540 — multiple unknown breakpoints. Relevance: 2000–2026 spans decimalization aftermath, Reg NMS (2007), the 2008 crisis, HFT rise, 2020 COVID, T+1 (2024). An "anomaly" that is really one regime's plumbing (e.g., pre-2010 latency) must be caught by sub-period analysis (expH), and Bai–Perron gives the formal tool.

6. Methodological rules adopted (feed Phase 9)#

  1. Every test statistic ships with a block/stationary-bootstrap CI, block length ≥ one trading day for intraday data.
  2. Hurst/long-memory claims: Lo (1991) modified R/S only, with bounce and staleness nulls.
  3. Granger tests only on both-fresh subsamples with staleness-matched nulls.
  4. Sub-period grid pre-specified: 2000–07 / 2008–14 / 2015–19 / 2020–26 + Bai–Perron endogenous breaks as robustness.
  5. CPCV inside train/validation; single-touch holdout untouched until expH.