Hurst Exponent

Install and import#

npm install fintech-algorithms

import { hurstExponent } from "fintech-algorithms/geometric-chart-patterns/market-structure-breakouts-and-regimes/hurst-exponent";

Signature#

hurstExponent(input)

A rolling rescaled-range estimate: over each window of period closes it takes the range of the mean-adjusted cumulative sum, divides by the window's standard deviation, and reports log(R/S) / log(period).

Parameters#

Returns#

TopicResult

series and latest carry a single value key. The warm-up is period - 1 bars, so with the default ready_at is 19; value is additionally null on any window whose cumulative-deviation range or standard deviation is zero, which is what a perfectly flat stretch gives.

Warm-up#

The first period - 1 bars (19 by default) positions are null. The window spans indices i-period+1 through i inclusive, so index period - 1 is the first with a full window.

Errors#

• When period is supplied as a non-integer or as a value below 2 — throws Error
• When a bar's close is not a finite number — throws Error

Complexity: time O(n × period), space O(n).

Worked example#

executed Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.

Input#

{
  "bars": [
    {
      "timestamp": "2024-01-02",
      "basis": "synthetic-unadjusted",
      "open": 100,
      "high": 101.45,
      "low": 98.695,
      "close": 100,
      "volume": 750000,
      "benchmark": 200
    },
    {
      "timestamp": "2024-01-03",
      "basis": "synthetic-unadjusted",
      "open": 101.49111452,
      "high": 103.38381693,
      "low": 100.05480022,
      "close": 101.78791214,
      "volume": 795117,
      "benchmark": 200.56326135
    },
    {
      "timestamp": "2024-01-04",
      "basis": "synthetic-unadjusted",
      "open": 102.45519048,
      "high": 104.6701838,
      "low": 100.91147007,
      "close": 102.9549389,
      "volume": 840234,
      "benchmark": 201.11020913
    }
  ],
  "parameters": {}
}

Call#

hurstExponent(input)

Returns#

object with 9 fields: topic_id, title, state, ready, ready_at, series, latest, parameters, …

{
  "topic_id": "D08-F07-A09",
  "title": "Hurst Exponent",
  "state": "calculated",
  "ready": true,
  "ready_at": 19,
  "series": {
    "value": [null, null, null, null, null, null]
  },
  "latest": {
    "value": 0.6970566842387678
  },
  "parameters": {},
  "diagnostics": {
    "causal": true,
    "input_count": 96
  }
}

Diagrams#

Calculation flow#

flowchart LR
    A["ordered OHLC observations, explicit lookbacks and threshol"] --> B["Validate order, basis, and finite values"]
    B --> C["Apply the selected Hurst Exponent convention"]
    C --> D["Emit value, readiness, and diagnostics"]
    D --> E["Interpret descriptively; test outcomes separately"]
    B -->|invalid or insufficient| X["Withhold output with a reason"]

stateDiagram-v2
    [*] --> Waiting
    Waiting --> Ready: enough valid causal observations
    Waiting --> Rejected: malformed or unsupported input
    Ready --> Calculated: selected formula applied
    Calculated --> Interpreted: diagnostic and limitation retained
    Interpreted --> Ready: next observation arrives
    Rejected --> Waiting: corrected input and deterministic reset

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

• CFA Institute technical-analysis overview — see linked primary or authoritative record
• TA-Lib maintained source — see linked primary or authoritative record
• Long-Term Storage Capacity of Reservoirs — see linked primary or authoritative record
• Evidence decision
• Level 1 evidence map

The rest of the Market Structure, Breakouts, and Regimes family#

• Highest-High and Lowest-Low PrimitivesThe two rolling extremes every breakout rule is built on: the highest high and lowest low over a window of period bars ending…
• Single-Asset New-High/New-Low SignalFlags whether a single instrument's close has cleared the highest high or undercut the lowest low of the preceding period bars.
• Breakout StrengthExpresses how far a close sits beyond its Donchian channel in units of ATR, so a two-tick break in a quiet market and a two-tic…
• Donchian BreakoutThe Donchian channel over the preceding period bars plus the two breakout booleans it implies.
• Opening Range BreakoutFixes the high and low of the session's first opening_bars bars and then tests every later close against that frozen range.
• Price Compression IndexCompares short-horizon volatility to long-horizon volatility as 100 × ATR(short_period) / ATR(long_period).
• Range Expansion IndexScores directional conviction as the signed sum of close-to-close changes over period bars divided by the sum of their absolu…
• Fractal Dimension IndexCompares the total path length walked by close over a window against the straight-line span of that window, on a log scale, and…
• Efficiency RatioKaufman's ratio of net displacement to gross travel: the absolute change in close over period bars divided by the sum of the …
• Market Meanness IndexCounts how often close crosses the median of its own period-bar window and reports that as a percentage of the period - 1 o…
• Trend/Range Regime ClassifierLabels each bar trend, range or uncertain by requiring two independent readings to agree: efficiency ratio at or above 0.…
• Volatility Regime ClassifierComputes realized volatility as the standard deviation of simple close returns over period bars, then ranks each reading agai…
• Directional PersistenceMaps each bar to +1, -1 or 0 by the sign of its close-to-close change, sums those signs over period bars, and reports the abs…
• Swing Structure DetectorConfirms five-bar swing highs and lows and labels each one against the previous swing of the same kind - HH, LH, HL, LL…
• Higher-High/Lower-Low StructureReduces price to the higher-high / lower-low sequence traders read structure from, labelling each confirmed five-bar swing HH…
• Inside/Outside Bar StructureClassifies each bar against its immediate predecessor as inside (high not above and low not below), outside (high not below…
• Market EntropyTreats each bar as one of three states by the sign of its close change, then reports the Shannon entropy of the state distribut…