| name | hurst-exponent |
| description | Estimate the Hurst exponent for a single ticker's daily log returns using rescaled-range (R/S) analysis, and classify the series as mean_reverting (H < 0.45), random_walk (H in [0.45, 0.55]), or trending (H > 0.55). Reports per-block R/S values and a block-bootstrap confidence band around H. Companion to pairs-scanner: pairs handles two-name cointegration, hurst handles single-name persistence. Answers "is this name a mean-reversion setup or a momentum setup?" Requires Stocks Basic. Runs on the free tier. |
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
- Pull daily closes for the ticker over
lookback_days * 1.6
calendar days.
- Log returns = diff of log(close).
- 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.
- 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.
- OLS on log-log: fit
log(R/S(n)) = c + H * log(n). H is the
slope.
- Bootstrap: block-bootstrap (block length 20) 100 times, refit
H each iteration, report p5/p50/p95 of the H distribution.
- Classify by fixed thresholds (0.45 and 0.55) so the buckets
are stable across runs.
Foundations used
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.
