Ascending Triangle

Install and import#

npm install fintech-algorithms

import { detectAscendingTriangle } from "fintech-algorithms/geometric-chart-patterns/continuation-structures/ascending-triangle";

Signature#

detectAscendingTriangle(close, parameters)

Scans a close series for an ascending triangle - a flat ceiling sitting over a rising floor - and reports whether that shape is still forming, has broken out, or was rejected. The two boundaries are least-squares lines fitted through the confirmed swing highs and swing lows of a pivot window; the shape passes when the ceiling's relative slope is within flat_tolerance of zero, the floor's is at least min_slope, and the channel narrows by at least min_convergence. A close beyond either boundary by break_buffer within max_confirmation_bars of the last pivot ends the search, and only a bullish break confirms.

Parameters#

Returns#

{ pattern: string; state: string; reason: string; event: Detection | null; events: Detection[]; pivots: Pivot[]; parameters: Parameters }

An object carrying pattern, the overall state (searching, rejected, candidate or confirmed), the reason behind that state, the selected event, the events that reached confirmed, every alternating pivots entry found so far, and the resolved parameters. Each event holds pivot_indices, pivot_prices, pivot_types, candidate_available_index, confirmation_index, breakout_direction, expected_direction, subtype, upper_boundary, lower_boundary and a metrics map with upper_slope, lower_slope, upper_relative_slope, lower_relative_slope, upper_intercept, lower_intercept, width_start, width_end, convergence, parallel_gap, impulse, impulse_direction and formation_bars.

Errors#

• When close is not an array, or is empty — throws Error
• When any close value is not a finite number, or is not strictly positive — throws Error
• When parameters carries a key that is not one of the twelve in DEFAULTS — throws Error
• When pivot_left, pivot_right, pivots_per_side, max_pattern_bars, max_confirmation_bars or impulse_lookback is not a positive integer, or pivots_per_side is below 2 — throws Error
• When flat_tolerance, min_slope, parallel_tolerance, min_convergence, min_impulse or break_buffer is negative or not finite, or min_convergence or break_buffer is 1 or more — throws Error
• When fewer than pivots_per_side * 2 alternating pivots have been confirmed — returns state searching rather than throwing

Complexity: time O(n * (pivot_left + pivot_right)), space O(n).

Worked example#

executed This entry is a thin wrapper its test never calls directly, so it was invoked with the arguments its shared implementation received. Real output, not asserted against a published figure.

Input#

[90, 91.75, 93.5, 95.25, 97, 98.75]

Showing 6 of 96 elements.

Call#

detectAscendingTriangle(close, parameters)

Returns#

object with 7 fields: pattern, state, reason, event, events, pivots, parameters

{
  "pattern": "ascending_triangle",
  "state": "confirmed",
  "reason": "breakout-confirmed",
  "event": {
    "pattern": "ascending_triangle",
    "state": "confirmed",
    "reason": "breakout-confirmed",
    "pivot_indices": [16, 22, 28, 34, 40, 46],
    "pivot_prices": [118, 108, 118.1, 112, 118, 115],
    "pivot_types": ["high", "low", "high", "low", "high", "low"],
    "candidate_available_index": 48,
    "confirmation_index": 49,
    "breakout_direction": "bullish",
    "expected_direction": "bullish",
    "subtype": null,
    "upper_boundary": 118.03333333333335,
    "lower_boundary": 116.04166666666667,
    "metrics": {
      "upper_slope": 0,
      "lower_slope": 0.2916666666666667,
      "upper_relative_slope": 0,
      "lower_relative_slope": 0.0025395443331882165,
      "upper_intercept": 118.03333333333335,
      "lower_intercept": 101.75,
      "width_start": 11.616666666666674,
      "width_end": 2.8666666666666742,
      "convergence": 0.7532281205164988,
      "parallel_gap": 0.0025395443331882165,
      "impulse": 0.21649484536082475,
      "impulse_direction": "bullish",
      "formation_bars": 30
    }
  },
  "events": [
    {
      "pattern": "ascending_triangle",
      "state": "confirmed",
      "reason": "breakout-confirmed",
      "pivot_indices": [16, 22, 28, 34, 40, 46],
      "pivot_prices": [118, 108, 118.1, 112, 118, 115],
      "pivot_types": ["high", "low", "high", "low", "high", "low"],
      "candidate_available_index": 48,
      "confirmation_index": 49,
      "breakout_direction": "bullish",
      "expected_direction": "bullish",
      "subtype": null,
      "upper_boundary": 118.03333333333335,
      "lower_boundary": 116.04166666666667,
      "metrics": {
        "upper_slope": 0,
        "lower_slope": 0.2916666666666667,
        "upper_relative_slope": 0,
        "lower_relative_slope": 0.0025395443331882165,
        "upper_intercept": 118.03333333333335,
        "lower_intercept": 101.75,
        "width_start": 11.616666666666674,
        "width_end": 2.8666666666666742,
        "convergence": 0.7532281205164988,
        "parallel_gap": 0.0025395443331882165,
        "impulse": 0.21649484536082475,
        "impulse_direction": "bullish",
        "formation_bars": 30
      }
    }
  ],
  "pivots": [
    {
      "kind": "high",
      "index": 16,
      "confirmation_index": 18,
      "price": 118
    },
    {
      "kind": "low",
      "index": 22,
      "confirmation_index": 24,
      "price": 108
    },
    {
      "kind": "high",
      "index": 28,
      "confirmation_index": 30,
      "price": 118.1
    }
  ],
  "parameters": {
    "pivot_left": 2,
    "pivot_right": 2,
    "pivots_per_side": 3,
    "max_pattern_bars": 44,
    "max_confirmation_bars": 4,
    "impulse_lookback": 12,
    "flat_tolerance": 0.00045,
    "min_slope": 0.00022,
    "parallel_tolerance": 0.00035,
    "min_convergence": 0.18,
    "min_impulse": 0.055,
    "break_buffer": 0.001
  }
}

Other exports#

This module also exports traceAscendingTriangle. Every module additionally exports run as an alias of its primary function, and a meta object carrying its catalog id, domain, family, shape and article URL.

Diagrams#

Calculation flow#

flowchart LR
    A["Finalized close arrives"] --> B["Confirm strict pivots after right-window delay"]
    B --> C{"Six alternating pivots available?"}
    C -->|No| S["SEARCHING"]
    C -->|Yes| D["Fit upper and lower boundaries"]
    D --> E{"Topic geometry contract passes?"}
    E -->|No| R["REJECTED with reason"]
    E -->|Yes| K["CANDIDATE at latest pivot confirmation"]
    K --> F{"Later strict buffered crossing?"}
    F -->|Accepted side| G["CONFIRMED"]
    F -->|Opposite side or expired| R
    F -->|Not yet| K

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#

• Foundations of Technical Analysis — Andrew W. Lo, Harry Mamaysky, and Jiang Wang
• SciPy `find_peaks` — SciPy project
• The Probability of Backtest Overfitting — David H. Bailey, Jonathan M. Borwein, Marcos López de Prado, and Qiji Jim Zhu
• Applicability decision

The rest of the Continuation Structures family#

• Descending TriangleScans a close series for a descending triangle - a falling ceiling pressing down on a flat floor - and reports whether that sha…
• Symmetrical TriangleScans a close series for a symmetrical triangle - a falling ceiling and a rising floor closing on each other - and reports whet…
• FlagScans a close series for a flag - a strong prior move followed by a narrow channel drifting against it - and reports whether th…
• PennantScans a close series for a pennant - a strong prior move followed by a small converging triangle - and reports whether that sha…
• Rising/Falling WedgeScans a close series for a wedge - two boundaries tilted the same way while converging - and reports whether that shape is stil…