fintech-algorithms

Markov-Switching Autoregression

Install and import

bash
npm install fintech-algorithms
ts
import { runFilter } from "fintech-algorithms/statistical-time-series/state-and-regime-models/markov-switching-autoregression";

Signature

runFilter(observations, config)

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

observations
[
  -0.0710447869,
  0.2119198541,
  0.4036856432,
  0.1288063984,
  0.0072781565,
  0.2691322581
]

Showing 6 of 160 elements.

config
{
  "transition": [
    [0.95, 0.05],
    [0.1, 0.9]
  ],
  "intercepts": [0.12, -0.18],
  "phis": [0.72, -0.3],
  "stds": [0.35, 1.05],
  "initial": [0.85, 0.15]
}

Call

runFilter(observations, config)

Returns

array of 160 objects

[
  {
    "index": 0,
    "regime_0_forecast": 0.4285714285714285,
    "regime_1_forecast": -0.13846153846153844,
    "predicted_state_0": 0.8225,
    "predicted_state_1": 0.17750000000000002,
    "posterior_state_0": 0.8341333456896518,
    "posterior_state_1": 0.1658666543103482,
    "most_likely_state": 0,
    "next_mixture_forecast": 0.025391734996519682,
    "log_predictive_density": -0.9020034995504373
  },
  {
    "index": 1,
    "regime_0_forecast": 0.068847753432,
    "regime_1_forecast": -0.15868656393,
    "predicted_state_0": 0.809013343836204,
    "predicted_state_1": 0.19098665616379595,
    "posterior_state_0": 0.9255985027572549,
    "posterior_state_1": 0.0744014972427451,
    "most_likely_state": 0,
    "next_mixture_forecast": 0.2141318776960829,
    "log_predictive_density": -0.0872910496699388
  },
  {
    "index": 2,
    "regime_0_forecast": 0.272582294952,
    "regime_1_forecast": -0.24357595623,
    "predicted_state_0": 0.8867587273436666,
    "predicted_state_1": 0.11324127265633334,
    "posterior_state_0": 0.9636140438968227,
    "posterior_state_1": 0.03638595610317734,
    "most_likely_state": 0,
    "next_mixture_forecast": 0.3530523573178951,
    "log_predictive_density": -0.02238977910202937
  }
]

Showing 3 of 160 elements.

Diagrams

Markov-Switching Autoregression — diagnostic scorecard
Markov-Switching Autoregression — failure boundary
Markov-Switching Autoregression — family handoff
Markov-Switching Autoregression — scenario comparison
Markov-Switching Autoregression — state update
Markov-Switching Autoregression — uncertainty ledger

Calculation flow

Markov-Switching Autoregression Causal Update 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