fintech-algorithms

Kalman Filter

Install and import

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

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
[
  0.1740371542,
  0.7180296431,
  0.0364260071,
  -0.3580458703,
  0.3552038047,
  0.4311906307
]

Showing 6 of 160 elements.

config
{
  "a": 0.96,
  "h": 1,
  "q": 0.08,
  "r": 0.64,
  "initial_mean": 0,
  "initial_variance": 2
}

Call

runFilter(observations, config)

Returns

array of 160 objects

[
  {
    "index": 0,
    "predicted_mean": 0,
    "predicted_variance": 1.9232,
    "predicted_observation": 0,
    "innovation": 0.1740371542,
    "innovation_variance": 2.5632,
    "kalman_gain": 0.7503121098626716,
    "filtered_mean": 0.1305821843622971,
    "filtered_variance": 0.4801997503121099
  },
  {
    "index": 1,
    "predicted_mean": 0.12535889698780522,
    "predicted_variance": 0.5225520898876405,
    "predicted_observation": 0.12535889698780522,
    "innovation": 0.5926707461121947,
    "innovation_variance": 1.1625520898876405,
    "kalman_gain": 0.4494870332546945,
    "filtered_mean": 0.3917567123546219,
    "filtered_variance": 0.28767170128300446
  },
  {
    "index": 2,
    "predicted_mean": 0.376086443860437,
    "predicted_variance": 0.3451182399024169,
    "predicted_observation": 0.376086443860437,
    "innovation": -0.339660436760437,
    "innovation_variance": 0.985118239902417,
    "kalman_gain": 0.350331793609469,
    "filtered_mean": 0.25709259383197747,
    "filtered_variance": 0.22421234791006017
  }
]

Showing 3 of 160 elements.

Diagrams

Kalman Filter — diagnostic scorecard
Kalman Filter — failure boundary
Kalman Filter — family handoff
Kalman Filter — scenario comparison
Kalman Filter — state update
Kalman Filter — uncertainty ledger

Calculation flow

Kalman Filter 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