Hurst exponent

hurst-exponent

You hand over a ticker. The skill pulls 2 years of daily closes, computes log returns, runs R/S analysis across a log-spaced set of block sizes, and fits log(R/S) = c + H * log(n) by OLS. H is the slope. Classifies the series based on where H falls and adds a bootstrap confidence band so the reader can judge whether the classification is robust.

Interpretation

• H < 0.45: mean-reverting. Prices push back toward a centerline. Pair strategies, range trading, and z-score entries historically have structural edge. Utilities and staples names tend here.
• H in [0.45, 0.55]: random walk. No persistence. Neither trend nor mean-reversion strategies have edge from the tape alone.
• H > 0.55: trending / momentum. Prices tend to keep going. Breakout strategies and trend-following have structural edge. Growth names in a strong run often show this.

When to invoke

• "Is AAPL trending or reverting right now?"
• Deciding whether to use pairs-scanner or a breakout entry on a name
• Screening a watchlist for mean-reversion candidates before running z-score entries
• The user says "Hurst", "R/S", "persistence", "mean reverting or trending"

Not for: cross-sectional pair analysis (that's pairs-scanner). Not for regime detection at higher frequencies (this uses daily returns; intraday persistence would need tick data).

What you need

• A ticker (--ticker)
• MASSIVE_API_KEY exported
• Stocks Basic minimum

Optional:

• --lookback-days (default 504, ~2 years). Longer = tighter H but more risk of masking a recent regime shift. Minimum 80.
• --n-bootstrap (default 100): block-bootstrap iterations for the confidence band. Set to 0 to skip.
• --seed (default 42): RNG seed.

What you get back

Two output layers from one run.

Layer 1: canonical JSON. hurst_exponent, classification (mean_reverting / random_walk / trending), reasoning, bootstrap with p5/p50/p95 and n_valid, per_block_rs with (block_size, rs_mean) entries showing how R/S scales with block size, plus lookback and n_returns.

Layer 2: rendered note. Header + H + classification tag, bootstrap band, per-block R/S table, one-line Take with strategy implication.

How it works

1. Pull daily closes for the ticker over lookback_days * 1.6 calendar days.
2. Log returns = diff of log(close).
3. Block sizes: 12 log-spaced values from min_block=10 to max_block=N/4. N/4 is the standard upper bound; going higher gives fewer blocks per size and destabilizes the regression.
4. R/S per block size n:
   • Partition returns into non-overlapping blocks of length n.
   • For each block: center by mean, take cumulative sum, R = max - min of the cumsum, S = sample std. R/S = R/S.
   • Mean R/S across blocks.
5. OLS on log-log: fit log(R/S(n)) = c + H * log(n). H is the slope.
6. Bootstrap: block-bootstrap (block length 20) 100 times, refit H each iteration, report p5/p50/p95 of the H distribution.
7. Classify by fixed thresholds (0.45 and 0.55) so the buckets are stable across runs.

Foundations used

• massive-api-patterns for REST auth, retry, and daily aggs.

Output mode: note

Narrative note with a small per-block table. A single number (H) plus its confidence band and per-block trace reads better as a short structured note than a table.

Endpoints used

• GET /v2/aggs/ticker/{T}/range/1/day/{from}/{to}?adjusted=true One call per run.

Doesn't handle (yet)

• Multi-scale Hurst. Only one H per run. A rolling Hurst over N-day windows would show regime changes; queued as a companion.
• Detrended fluctuation analysis (DFA). R/S is the classic method; DFA is more robust to non-stationarities. Queued.
• Fractional differencing. If you want to trade on the estimate, the natural next step is fractional integration order d = H - 0.5. Beyond this skill's scope.
• Cross-asset Hurst comparison. No "AAPL's H vs sector median H." Queued.

These are clean PR extensions.