Fibonacci Pivot Points

Install and import#

npm install fintech-algorithms

import { fibonacciPivotPoints } from "fintech-algorithms/geometric-chart-patterns/pivots-and-levels/fibonacci-pivot-points";

Signature#

fibonacciPivotPoints(input)

Takes the same (H + L + C) / 3 pivot as the classic variant but places the bands at Fibonacci fractions of the previous bar's range: r1/s1 at 0.382 of it and r2/s2 at 0.618.

Parameters#

Returns#

TopicResult

series and latest carry pivot, r1, s1, r2 and s2. The warm-up is one bar, because every value is derived from the preceding bar.

Warm-up#

The first 1 bar positions are null. Index 0 is null across all five series; ready_at is 1 for any input of two or more bars.

Errors#

• When a bar's high is below its own open, close, or low (or low is above them) — throws Error
• When parameters is supplied as something other than a plain object — 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#

fibonacciPivotPoints(input)

Returns#

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

{
  "topic_id": "D08-F01-A06",
  "title": "Fibonacci Pivot Points",
  "state": "calculated",
  "ready": true,
  "ready_at": 1,
  "series": {
    "pivot": [
      null,
      100.04833333333333,
      101.74217643000001,
      102.84553092333333,
      103.11026585,
      102.75204238333333
    ],
    "r1": [
      null,
      101.10074333333334,
      103.01386081322,
      104.28135956819334,
      104.61482444292,
      104.21510088589334
    ],
    "s1": [
      null,
      98.99592333333332,
      100.47049204678002,
      101.40970227847332,
      101.60570725708001,
      101.28898388077333
    ],
    "r2": [
      null,
      101.75092333333333,
      103.79950875678001,
      105.16841600847333,
      105.54434231708001,
      105.11897996077333
    ],
    "s2": [
      null,
      98.34574333333333,
      99.68484410322002,
      100.52264583819333,
      100.67618938292,
      100.38510480589333
    ]
  },
  "latest": {
    "pivot": 101.55414906333333,
    "r1": 102.74645655493333,
    "s1": 100.36184157173332,
    "r2": 103.48306537173332,
    "s2": 99.62523275493334
  },
  "parameters": {},
  "diagnostics": {
    "causal": true,
    "input_count": 96
  }
}

Diagrams#

Calculation flow#

flowchart LR
    A["closed OHLC bars or causally confirmed pivots with session"] --> B["Validate order, basis, and finite values"]
    B --> C["Apply the selected Fibonacci Pivot Points 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 Pivots and Levels family#

• Causal Pivot DetectionFinds swing highs and lows using only bars that had already arrived.
• ZigZag SegmentationSegments a series into alternating swings that exceed a percentage threshold.
• Support/Resistance ClusteringGroups nearby pivots into levels.
• Robust Trendline FittingFits a trendline through pivots in log space with outlier resistance.
• Classic and Floor-Trader Pivot PointsProjects the classic floor-trader pivot and two resistance/support pairs for each bar from the previous bar's high, low, and cl…
• Camarilla Pivot PointsAnchors its bands on the previous bar's close rather than on the pivot: r1/s1 sit at close ± 1.1 × range / 12 and r2/`s…
• Woodie Pivot PointsWeights the current bar's open into the pivot, (H_prev + L_prev + 2 × open) / 4, then derives r1/s1 by reflecting that pi…
• DeMark Pivot PointsChooses one of three formulas for the intermediate X depending on whether the previous bar closed below, above, or level with…
• Rolling Support and ResistanceReports, for each bar, the lowest low and highest high of the period bars that came strictly before it.
• Fractal Support and ResistanceHolds the most recent confirmed five-bar fractal high and low forward as resistance and support.
• ATR Support and ResistancePlaces support and resistance a volatility-scaled distance either side of a simple moving average of close: `center ± multiplie…
• Pivot Range WidthMeasures the central pivot range rather than its bands: bottom is the previous bar's midpoint (H + L) / 2, top is that mi…