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AutocorrelationOptions

What an autocorrelation may be told.

public sealed record AutocorrelationOptions

Properties — Adjusted says whether lag k divides by n - k rather than by n; false by default, which is the reference's, and the estimator that keeps the sequence positive semi-definite. BartlettConfidenceInterval says whether the band widens with the lag by Bartlett's formula; true by default, which is the reference's — false gives the flat band a correlogram usually draws. ConfidenceLevel is the two-sided level the band is reported at; 0.95 by default.

Exceptions — ArgumentOutOfRangeException when ConfidenceLevel does not lie strictly inside (0, 1) — checked where the level is set, not where a band three functions later would otherwise reach the caller at the wrong width with no exception naming it.

Example — the estimator, the band shape, and the level: three independent choices on the same call.

using Lodestar.Stats.TimeSeries;

double[] series = [1.0, 3.0, 2.0, 5.0, 4.0, 7.0, 6.0, 9.0, 8.0, 11.0, 10.0, 13.0];

AutocorrelationResult biased = SerialCorrelation.Autocorrelation(series, lagCount: 4);
AutocorrelationResult adjusted = SerialCorrelation.Autocorrelation(
    series, lagCount: 4, new AutocorrelationOptions { Adjusted = true });

double r1Biased = Math.Round(biased.Values[1], 4);      // => 0.5922
double r1Adjusted = Math.Round(adjusted.Values[1], 4);  // => 0.646

Remarks — SerialCorrelation.PartialAutocorrelation reads only ConfidenceLevel from this type: Adjusted and BartlettConfidenceInterval have no meaning for a partial autocorrelation, so nothing here is silently ignored without saying so.

BartlettConfidenceInterval = false widens lag zero's band, which the default narrows to a point. Bartlett's formula is exactly zero at lag zero, so the default band's [1, 1] there matches the reference; the flat band applies its 1/n variance uniformly, lag zero included, because the reference's own non-Bartlett variance is a scalar rather than a per-lag formula.

using Lodestar.Stats.TimeSeries;

double[] series = [1.0, 3.0, 2.0, 5.0, 4.0, 7.0, 6.0, 9.0, 8.0, 11.0, 10.0, 13.0];

AutocorrelationResult flatBand = SerialCorrelation.Autocorrelation(
    series, lagCount: 4, new AutocorrelationOptions { BartlettConfidenceInterval = false });

double lower0 = Math.Round(flatBand.ConfidenceLower[0], 4);  // => 0.4342
double upper0 = Math.Round(flatBand.ConfidenceUpper[0], 4);  // => 1.5658

Being a record, two option sets with the same three values are equal.

Applies to — net10.0, netstandard2.0.

See also — SerialCorrelation.Autocorrelation, SerialCorrelation.PartialAutocorrelation, AutocorrelationResult, the Python equivalence table.