Calculates the autocorrelation using the FFT method.
FACORR(series, norm)
series 
 
A series or array. 

norm 
 
Optional. An integer, the normalization method:

A series.
W1: gsin(1000, .001, 4)
W3: acorr(w1)
performs the autocorrelation of a sine wave. The peaks of the result indicate the series is very similar to itself at the time intervals where the peaks occur, i.e. the series is periodic.
W1: gsin(1000, .001, 4)
W2: gnorm(1000, .001)
W3: facorr(W1, 1)
W4: facorr(W2, 1)
W3 displays the autocorrelation of a sine wave normalized to 1 and 1. W4 shows the normalized autocorrelation of random noise.
The normalized maximum of both results 1.0 at time t = 0, indicating the expected perfect correlation 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 autocorrelation for a random process is defined as:
where E is the expected value operator, x[n] is a stationary random process and * indicates complex conjugate. In practice, the autocorrelation is estimated because only a finite sample of an infinite duration random process is available. The estimate of the autocorrelation function for a series of length N is defined as:
FACORR performs correlation by computing the FFT of the input series.
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 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 autocorrelation is used to determine how similar a series is to itself or if a series is periodic.
See ACORR for the time domain implementation.
See FACOV to remove the mean from the input series before calculating the autocorrelation.