Hilbert Transform Dominant Cycle Period

Install and import#

npm install fintech-algorithms

import { hilbertTransformDominantCyclePeriod } from "fintech-algorithms/statistical-time-series/hilbert-and-ehlers-cycle-analytics/hilbert-transform-dominant-cycle-period";

Signature#

hilbertTransformDominantCyclePeriod(input)

Estimates the dominant cycle length in bars from the bar-to-bar change in the Hilbert phase angle, clamping each raw estimate into the 6-to-50 bar range and smoothing it with a 0.2 / 0.8 exponential update. Any contract failure is rethrown as an Error whose message begins topic calculation failed: .

Parameters#

Returns#

TopicResult

series.value and latest.value carry the smoothed dominant-cycle period measured in bars, always between 6 and 50. parameters echoes the supplied parameters and diagnostics reports causal and input_count. Warm-up is seven leading nulls, so ready_at is 7.

Warm-up#

The first 7 positions are . The 4-bar EMA of close first resolves at index 3, the four-tap quadrature filter needs three further bars so phase begins at index 6, and the period step differences two consecutive phases, which puts the first estimate and ready_at at index 7.

Errors#

• When parameters.period is present but is not an integer of at least 4 — throws Error
• When bars is empty, a timestamp is missing or not strictly increasing, an OHLCV field is not finite, volume is negative, or high and low do not bracket open and close — throws Error

Complexity: time O(n), 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#

hilbertTransformDominantCyclePeriod(input)

Returns#

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

{
  "topic_id": "D09-F06-A01",
  "title": "Hilbert Transform Dominant Cycle Period",
  "state": "calculated",
  "ready": true,
  "ready_at": 7,
  "series": {
    "value": [null, null, null, null, null, null]
  },
  "latest": {
    "value": 24.86605208112273
  },
  "parameters": {},
  "diagnostics": {
    "causal": true,
    "input_count": 96
  }
}

Diagrams#

Calculation flow#

flowchart LR
    A["uniformly sampled finite prices with declared prefilter, c"] --> B["Validate order, basis, and finite values"]
    B --> C["Apply the selected Hilbert Transform Dominant Cycle Period 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 cycle indicator group — see linked primary or authoritative record
• SciPy analytic-signal documentation — 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 Hilbert and Ehlers Cycle Analytics family#

• Hilbert Transform Dominant Cycle PhaseReturns the instantaneous Hilbert phase angle in radians as atan2(quadrature, in_phase), where both components come from a fo…
• Hilbert Transform Phasor ComponentsExposes the raw phasor behind the Hilbert cycle family: the in-phase component, its quadrature partner from the four-tap filter…
• Hilbert Transform SineWaveTurns the Hilbert phase angle into the classic sinewave pair, the sine of the phase and a lead sine shifted a quarter turn ahea…
• Hilbert Transform Trend/Cycle ModeLabels each bar trend or cycle by asking whether the distance from close to its exponential trend exceeds 1.5 times the c…
• Ehlers Cyber CycleRuns close through a two-pole high-pass filter tuned to period, then smooths the residual with an EMA of the same span, lea…
• Ehlers Roofing FilterStacks the two halves of a roof: a two-pole high-pass filter tuned to period removes the slow drift, and an Ehlers Super Smoo…
• Ehlers DecyclerSubtracts a two-pole high-pass residual from close, leaving a trend line with the sub-period wiggle removed and far less la…