Calculates the
ACOV(series, norm)
series 
 
A series or array.  
norm 
 
Optional. An integer, the normalization method:

A series.
W1: gsin(1000, .001, 4)
W3: acov(W1)
performs the
W1: gsin(1000, .001, 4)
W2: gnorm(1000, .001)
W3: acov(W1, 1)
W4: acov(W2, 1)
W3 displays the
The normalized maximum of both results is 1.0 at time t = 0, indicating the expected perfect covariance at time t = 0 (true for all series).
The series of W4 displays only one distinct peak at t = 0, indicating that W2 is not correlated with itself and is nonperiodic.
Both series display a triangular envelope due to the assumption that the input series is zero before the first sample and after the last sample.
The
where E is the expected value operator, x[n]
is a stationary random process, μ_{x} is the mean value and * indicates
complex conjugate. In practice, the
where:
ACOV performs
The output length L is:
L = 2 * length(s)  1
The zeroth lag component is the mid point of the series.
The BIASED normalization divides the result by N, the maximum length of the input series.
The UNBIASED normalization divides the result by
N  abs(N  i  1) + 1
where i is the index of the result with a start value of 1. For a 0 start index, the unbiased estimate becomes:
The
See FACOV for the frequency domain implementation.