GJR-GARCH

Install and import#

npm install fintech-algorithms

import { calculate } from "fintech-algorithms/volatility-and-covariance/conditional-volatility/gjr-garch";

Signature#

calculate(data)

Isolate the extra term activated by a negative lagged residual. Supplied-parameter educational reference; no fitted performance claim.

Parameters#

Returns#

TopicResult

Structured result with readiness, values, parameters, and diagnostics.

Warm-up#

The first depends on window or model order positions are null prefix until minimum history exists.

Errors#

• When required data is missing, non-finite, malformed, or out of range — raises ContractError / Error

Complexity: time O(n), space Full diagnostic trace retained for teaching; see implementation for observation/window/matrix dimensions.

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#

{
  "returns": [-0.02, 0.01, 0],
  "parameters": {
    "omega": 0.000002,
    "initial_variance": 0.0001,
    "alpha": 0.1,
    "beta": 0.8,
    "gamma": 0.1
  }
}

Call#

calculate(data)

Returns#

object with 8 fields: topic_id, title, parameters, series, latest, ready, ready_at, diagnostics

{
  "topic_id": "D10-F03-A04",
  "title": "GJR-GARCH",
  "parameters": {
    "omega": 0.000002,
    "initial_variance": 0.0001,
    "alpha": 0.1,
    "beta": 0.8,
    "gamma": 0.1
  },
  "series": [
    {
      "index": 0,
      "variance": 0.0001,
      "initialization": true
    },
    {
      "index": 1,
      "variance": 0.00016200000000000003,
      "intercept": 0.000002,
      "shock_contribution": 0.00004,
      "threshold_contribution": 0.00004,
      "carry": 0.00008
    },
    {
      "index": 2,
      "variance": 0.00014160000000000003,
      "intercept": 0.000002,
      "shock_contribution": 0.00001,
      "threshold_contribution": 0,
      "carry": 0.00012960000000000003
    }
  ],
  "latest": {
    "index": 2,
    "variance": 0.00014160000000000003,
    "intercept": 0.000002,
    "shock_contribution": 0.00001,
    "threshold_contribution": 0,
    "carry": 0.00012960000000000003
  },
  "ready": true,
  "ready_at": 0,
  "diagnostics": {
    "causal": true,
    "input_count": 3,
    "fitted_parameters": false,
    "model": "gjr_garch"
  }
}

Diagrams#

Calculation flow#

flowchart TD
    N0["Read previous residual sign"]
    N1["Compute ordinary squared-shock term"]
    N2["Activate γ term only below zero"]
    N3["Add intercept and carried variance"]
    N0 --> N1 --> N2 --> N3

flowchart TD
    A["Supplied observations and parameters"] --> B{"Contract valid?"}
    B -->|No| E["Reject with explicit error"]
    B -->|Yes| C{"Required history available?"}
    C -->|No| W["Withhold; never insert zero"]
    C -->|Yes| D["GJR-GARCH calculation"]
    D --> F["Inspect diagnostics and stated limits"]

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#

• Scope of evidence

The rest of the Conditional Volatility family#

• ARCHFollow a squared shock through a finite coefficient queue.
• GARCHSeparate new shock information from carried variance.
• EGARCHCompare signed standardized shocks on the log-variance scale.
• FIGARCHKeep retained fractional weights and omitted backcast mass separate.
• HAR-RVWatch one elevated session enter and leave three overlapping horizons.