fintech-algorithms

Hidden Markov Model

Install and import

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

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
[
  -0.9183368993,
  -0.5364890278,
  -0.550167602,
  -1.0221111597,
  -0.9348142289,
  -0.5355520167
]

Showing 6 of 160 elements.

config
{
  "transition": [
    [0.94, 0.06],
    [0.12, 0.88]
  ],
  "means": [-0.15, 0.25],
  "stds": [0.55, 1.45],
  "initial": [0.8, 0.2]
}

Call

runFilter(observations, config)

Returns

array of 160 objects

[
  {
    "index": 0,
    "predicted_state_0": 0.776,
    "predicted_state_1": 0.22400000000000003,
    "posterior_state_0": 0.8264612333826495,
    "posterior_state_1": 0.17353876661735046,
    "most_likely_state": 0,
    "log_predictive_density": -1.3598732483743445
  },
  {
    "index": 1,
    "predicted_state_0": 0.7976982113737725,
    "predicted_state_1": 0.20230178862622736,
    "posterior_state_0": 0.9039212244809284,
    "posterior_state_1": 0.09607877551907154,
    "most_likely_state": 0,
    "log_predictive_density": -0.6930121943884898
  },
  {
    "index": 2,
    "predicted_state_0": 0.8612154040743613,
    "predicted_state_1": 0.13878459592563866,
    "posterior_state_0": 0.9359801579550975,
    "posterior_state_1": 0.0640198420449025,
    "most_likely_state": 0,
    "log_predictive_density": -0.6690356366768324
  }
]

Showing 3 of 160 elements.

Diagrams

Hidden Markov Model — diagnostic scorecard
Hidden Markov Model — failure boundary
Hidden Markov Model — family handoff
Hidden Markov Model — scenario comparison
Hidden Markov Model — state update
Hidden Markov Model — uncertainty ledger

Calculation flow

Hidden Markov Model 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