Bayesian Change-Point Detection

Install and import#

npm install fintech-algorithms

import { runFilter } from "fintech-algorithms/statistical-time-series/state-and-regime-models/bayesian-change-point-detection";

Signature#

runFilter(observations, config)

Online detection of structural breaks by tracking the posterior over run length — how long since the last change. Unlike a regime model it does not need the number of regimes specified in advance.

Parameters#

Returns#

{ …per-step run-length posterior }[]

The run-length distribution per observation. Being online, an apparent change point can be revised by later data — the posterior shows that, a hard list of breaks would not.

Errors#

• When hazard falls outside 0…1, or a variance is not positive — throws

Complexity: time O(n²), space O(n).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

[-0.3275053489, 0.2452664583, 0.224748597]

{
  "hazard": 0.025,
  "observation_variance": 0.36,
  "prior_mean": 0,
  "prior_variance": 4
}

Call#

runFilter(observations, config)

Returns#

object with 1 field: 2

{
  "2": {
    "index": 2,
    "change_probability": 0.00942784148480789,
    "map_run_length": 3,
    "expected_run_length": 2.9241612404581354,
    "active_hypotheses": 4,
    "map_mean": 0.04611964608414239,
    "log_predictive_density": -0.6857585614486436
  }
}

Diagrams#

Calculation flow#

flowchart LR
    A["Filtered state at t-1"] --> B["Predict state at t"]
    B --> C["Read observation available at t"]
    C --> D["Compute evidence or innovation"]
    D --> E["Normalize or gain-weight update"]
    E --> F["Filtered state at t"]
    F --> G["Publish diagnostics"]
    F --> A

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#

• Bayesian Online Changepoint Detection — Ryan Prescott Adams and David J. C. MacKay
• Strictly Proper Scoring Rules, Prediction, and Estimation — Tilmann Gneiting and Adrian E. Raftery

The rest of the State and Regime Models family#

• Kalman FilterOptimal recursive estimation of a hidden state from noisy observations in a linear Gaussian system.
• Extended Kalman FilterThe Kalman filter for non-linear systems, linearised at each step.
• Unscented Kalman FilterPropagates a set of deterministically chosen sigma points through the non-linearity instead of linearising it.
• Hidden Markov ModelInfers a discrete hidden regime from observations.
• Markov-Switching AutoregressionAn autoregression whose coefficients switch with a hidden regime.