Vector.AutoCorrUnBiased Method

function AutoCorrUnBiased(const Vec: TVec; Lags: Integer): TVec;

Unbiased auto-correlation.

#	Name	Type	Description
1	Vec	TVec
2	Lags	Integer

Result: stored in self (calling object), returns self for chaining

Remarks:

Calculate the unbiased auto-correlation of the vector Vec. The result of Length = Lags is stored in the calling vector (V). The Lags parameter must be equal or smaller than the calling vector (V) length. The unbiased auto-correlation is defined by the following equation:

\begin{aligned} \text{V}[k] &= \frac{1}{\text{Length}-|n|} \sum _{k=0} ^{\text{Length}-1} \text{Vec}[k] \cdot \text{Vec}[k+n] ,\quad \text{where } 0 \leq k \leq \text{Lags} \\ \text{Vec}[k] &= \begin{cases} \text{Vec}[k] & 0\leq k \leq \text{Length} \\ 0 & \text{otherwise} \end{cases} \end{aligned}

Examples

var a,b: Vector;
begin
    a.SetIt(False,[1,2,3,4]);
    b.AutoCorrUnBiased(a,2);
end;

See Also: Vector.AutoCorrBiased, Vector.AutoCorrNormal