SeriesAutocovariance Method (IReadOnlyListDouble, Int32)

public static double Autocovariance(
	this IReadOnlyList<double> series,
	int lag
)

<ExtensionAttribute>
Public Shared Function Autocovariance ( 
	series As IReadOnlyList(Of Double),
	lag As Integer
) As Double

public:
[ExtensionAttribute]
static double Autocovariance(
	IReadOnlyList<double>^ series, 
	int lag
)

[<ExtensionAttribute>]
static member Autocovariance : 
        series : IReadOnlyList<float> * 
        lag : int -> float 

Parameters

series

Type: System.Collections.GenericIReadOnlyListDouble
The data series from which to compute the auto-covariance.

lag

Type: SystemInt32
The lag at which to compute the auto-covariance.

Return Value

Usage Note

In a length-N time series, there are N-k lag-k observations. Nonetheless, the definition of the lag-k auto-covariance requires division by N, not N-k. This counterintuitive convention ensures that the auto-covariance has desirable positive definiteness properties and agrees with the computation via FFT.

The computation of an auto-covariance via this method is O(N). If you need to compute more than a handful of auto-covariances, it is more efficient to call the Autocovariance(IReadOnlyListDouble), which computes all of them in O(N log N).

While the sample auto-covariance does converge to the population auto-covariance in the large-N limit, this convergence is very slow. If you want an estimate of the population auto-covariance, use SeriesPopulationStatistics(IReadOnlyListDouble) to obtain a much better estimate.

Reference