ACF
Install and import#
npm install fintech-algorithmsimport { acf } from "fintech-algorithms/statistical-time-series/diagnostics/acf";Signature#
acf(values, maxLag)Autocorrelation at each lag. The first diagnostic to run on any series you intend to model: it shows whether there is structure to model at all, and slow decay is the classic signature of non-stationarity.
Parameters#
| Name | Type | Notes |
|---|---|---|
values | number[] | Observation series in chronological order, oldest first. |
maxLag | number | Highest lag to compute. Beyond roughly n/4 the estimates are too noisy to read. min: 1 · integer: true |
Returns#
{ method, variant, nobs, max_lag, mean, denominator, numerators, coefficients, confidence_bands }
Coefficients with the numerator and denominator used — estimators differ in whether the denominator varies with lag, and the two conventions give visibly different plots.
Errors#
- When maxLag is not less than the sample size — throws
Complexity: time O(n × maxLag),
space O(maxLag).
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#
[0.49366418, 1.54242291, -0.82556495, 0.47513288, 0.50704417, -0.3816439]Showing 6 of 96 elements.
12Call#
acf(values, maxLag)Returns#
object with 11 fields: method, variant, nobs, max_lag, mean, denominator, numerators, coefficients, …
{
"method": "acf",
"variant": "centered-unadjusted-direct",
"nobs": 96,
"max_lag": 12,
"mean": 0.29779557927083333,
"denominator": 153.9714722414195,
"numerators": [
153.9714722414195,
102.29629606088473,
67.86612357881646,
43.864068660314665,
13.159013573869158,
-12.01222465335103
],
"coefficients": [
1,
0.6643847368068891,
0.4407707648102877,
0.28488438813871975,
0.08546397187939134,
-0.07801591085987973
],
"confidence_95": 0.2000416623272929,
"state": "estimated",
"reason": "finite centered series with nonzero variance"
}Other exports#
This module also exports
pacf, adf, kpss, ljungBox, zivotAndrews, runDiagnostic. 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#
Calculation flow#
ACF decision flow
flowchart TD
A["Ordered finite series"] --> B{"Contract valid?"}
B -- "No" --> X["Stop: explicit invalid state"]
B -- "Yes" --> C["Center once"]
C --> D["Align lag-k pairs"]
D --> E["Divide by common sum of squares"]
E --> F["Inspect coefficient and heuristic band"]
F --> G{"Declared strict decision rule"}
G --> H["Report machine state, null, and limitation"]
H --> I["Compare with PACF"]
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.
References#
- statsmodels.tsa.stattools.acf
- Evidence decisions