Random Walk Index (High/Low)

Install and import#

npm install fintech-algorithms

import { randomWalkIndexHighLow } from "fintech-algorithms/technical-indicators/trend-systems/random-walk-index-high-low";

Signature#

randomWalkIndexHighLow(input)

Scores how far price has travelled against what a random walk would explain, by taking the largest displacement-over-expected-range ratio across every lookback length from 2 up to period, once upward and once downward.

Parameters#

Returns#

TopicResult

series and latest carry high and low, the upward and downward random-walk scores, and no combined line. Both share one warm-up.

Warm-up#

The first period bars (14 by default) positions are null. The scan starts at index period because the longest lookback reaches that far back, so with the default period indices 0 to 13 are null and ready_at is 14.

Errors#

• When parameters.period is present but is not an integer of at least 2 — throws Error
• When bars is empty, or a bar has a non-finite price, a negative volume, a timestamp not greater than the previous one, or a high below its open, low, or close — throws Error

Complexity: time O(n * period^2), 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#

randomWalkIndexHighLow(input)

Returns#

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

{
  "topic_id": "D07-F02-A16",
  "title": "Random Walk Index (High/Low)",
  "state": "calculated",
  "ready": true,
  "ready_at": 14,
  "series": {
    "high": [null, null, null, null, null, null],
    "low": [null, null, null, null, null, null]
  },
  "latest": {
    "high": 0.16740171878302448,
    "low": 1.3252890024447201
  },
  "parameters": {},
  "diagnostics": {
    "causal": true,
    "input_count": 96
  }
}

Diagrams#

Calculation flow#

flowchart LR
    A["ordered OHLC or close observations with explicit window, s"] --> B["Validate order, basis, and finite values"]
    B --> C["Apply the selected Random Walk Index (High/Low) 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#

• TA-Lib function groups — see linked primary or authoritative record
• TA-Lib C/C++ API — see linked primary or authoritative record
• TA-Lib maintained source — see linked primary or authoritative record
• Evidence decision
• Level 1 evidence map

The rest of the Trend Systems family#

• MACDMoving average convergence/divergence: the gap between a fast and a slow EMA, its own EMA as a signal line, and the difference …
• Percentage Price Oscillator (PPO)MACD expressed as a percentage of the slow EMA rather than in price units, which makes readings comparable across instruments a…
• Aroon Up, Down, and OscillatorMeasures how recently the highest high and lowest low occurred within the lookback, expressed as 0–100.
• Directional MovementThe components beneath ADX: directional movement in each direction, Wilder-smoothed, divided by the average true range to give …
• Average Directional Index (ADX)Average directional index: the smoothed magnitude of the gap between +DI and −DI.
• Ichimoku CloudThe five Ichimoku lines.
• Parabolic SARStop-and-reverse: a trailing stop that accelerates toward price while a trend persists and flips side when price crosses it.
• SupertrendAn ATR-scaled band around the median price that ratchets in the direction of the trend and only flips when close crosses it.
• Average Directional Index Rating (ADXR)Runs the Wilder directional-movement system over the bars and returns the smoothed plus_di, minus_di and adx lines togeth…
• Vortex Indicator (+VI/−VI)Sums the upward and downward vortex movements over a rolling window and divides each by the summed true range, giving the paire…
• Choppiness IndexCompares the summed true range over a window against the window's own high-to-low span, on a base-10 log scale normalised by th…
• Trend Intensity IndexSplits each close into the part above and the part below a simple moving average, sums each part over a second window, and repo…
• QStickAverages the candle body, close minus open, over a rolling window, so a positive reading means the window closed above its open…
• Mass IndexTakes the ratio of a 9-period EMA of the high-low range to the 9-period EMA of that EMA, then sums the ratio over a longer wind…
• Vertical Horizontal FilterDivides the highest-to-lowest close span over a window by the sum of the absolute bar-to-bar close changes in that same window,…
• Trend Trigger FactorCompares the current window's high and low against the immediately prior window's, and reports the buy-minus-sell power as a pe…
• Directional Trend IndexWilder-smooths the net of the upward high moves against the downward low moves, and divides it by the smoothed total of both, g…
• Trend Strength IndexMeasures the absolute gap between a fast and a slow EMA of the close in units of average true range, so the spread is comparabl…