Rolling Beta

Install and import#

npm install fintech-algorithms

import { rollingBeta } from "fintech-algorithms/technical-indicators/rolling-statistical-indicators/rolling-beta";

Signature#

rollingBeta(input)

Regresses the asset's simple returns on the benchmark's over a trailing window and returns the slope, using the population covariance and variance of the window.

Parameters#

Returns#

TopicResult

series and latest carry a single beta key; the intercept is not emitted by this topic. A bar is null when the benchmark returns in its window have zero variance. Returns cost one bar, which lengthens the warm-up by one over a plain window.

Warm-up#

The first period bars (20 by default) positions are null. Both return series start at index 1, so the first window with period paired returns closes at index period: with the default period indices 0 to 19 are null and ready_at is 20.

Errors#

• When any bar omits benchmark, so the benchmark return series cannot be built — throws Error
• When a bar's benchmark is present but is not a finite number, or is not greater than zero — throws Error
• 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), 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#

rollingBeta(input)

Returns#

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

{
  "topic_id": "D07-F09-A03",
  "title": "Rolling Beta",
  "state": "calculated",
  "ready": true,
  "ready_at": 20,
  "series": {
    "beta": [null, null, null, null, null, null]
  },
  "latest": {
    "beta": -5.216643800648915
  },
  "parameters": {},
  "diagnostics": {
    "causal": true,
    "input_count": 96
  }
}

Diagrams#

Calculation flow#

flowchart LR
    A["time-aligned observations, window length, minimum count, e"] --> B["Validate order, basis, and finite values"]
    B --> C["Apply the selected Rolling Beta 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 Rolling Statistical Indicators family#

• Rolling PercentileReports where the current close sits inside its own trailing window, as the percentage of window values below it plus a configu…
• Rolling QuantileReturns the requested quantile of the close over a trailing window, sorting each window and interpolating linearly between the …
• Rolling AlphaRuns the same trailing regression of asset returns on benchmark returns as rolling beta, and returns the intercept, the mean as…