Baxter-King Filter

Install and import

bash

npm install fintech-algorithms

import { bkFilter } from "fintech-algorithms/statistical-time-series/decomposition-and-cycles/baxter-king-filter";

Signature

bkFilter(values, low, high, K)

A band-pass filter isolating fluctuations between two periodicities. Being a symmetric moving average it consumes K observations at **each** end, so the filtered series is shorter than the input at both.

Parameters

Name	Type	Notes
`values`	`number[]`	Observation series.
`low`	`number`	Shortest cycle length to retain, in periods. min: 1 · integer: true
`high`	`number`	Longest cycle length to retain. min: 1 · integer: true
`K`	`number`	Filter half-length. Larger sharpens the band and costs more observations at each end. min: 1 · integer: true

Returns

{ cycle, weights, trimmed }

The band-passed series with the weights used and how many observations were trimmed from each end.

Errors

When low ≥ high, or the series is shorter than 2K + 1 — throws

Complexity: time O(n × K), space O(n).

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

values

[
  100.0901805654,
  101.3367333472,
  102.4083163971,
  102.9128416721,
  103.198587938,
  102.4311805579
]

Showing 6 of 192 elements.

low

high

Call

bkFilter(values, low, high, K)

Returns

object with 8 fields: cycle, trend, weights, low_period, high_period, K, edge_loss_each_side, weight_sum

{
  "cycle": [null, null, null, null, null, null],
  "trend": [null, null, null, null, null, null],
  "weights": [
    -0.011925074099926311,
    -0.042289342849822956,
    -0.050142927835196305,
    -0.02785666762175208,
    0.0015008360109016001,
    0.0016130582107286165
  ],
  "low_period": 6,
  "high_period": 32,
  "K": 12,
  "edge_loss_each_side": 12,
  "weight_sum": 9.71445146547012e-17
}

Other exports

This module also exports stlDecompose, hpFilter, cfFilter, fftPeriodogram, haarWavelet, runTopic. Every module additionally exports run as an alias of its primary function, and a meta object carrying its catalog id, domain, family, shape and article URL.

Diagrams

Baxter-King Filter — scenario comparison

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

Evidence table
Source records
Evidence policy
Version notes