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See also: introduction to autocorrelation |
The autocorrelation is calculated in the same way as the correlation between two variables (just using the same variable twice). If we consider time signals, the values of the autocorrelation may be calculated by shifting one of the two formal variables by a certain amount Dt. If we plot the results of these calculations against the time shift, we obtain the autocorrelation function, or autocorrelogram. Here's an which shows the principal function of an autocorrelogram.
The idea is that a time-series y_{t} (with the measurements
x_{1}, x_{2}, x_{3}, ..., x_{n}) is correlated
with itself. In the first step, the pairs to be correlated are:
First Series | x_{1} | x_{2} | x_{3} | ... | x_{n} |
Second Series | x_{1} | x_{2} | x_{3} | ... | x_{n} |
The correlation coefficient is obviously 1. In the next step, the second
series is shifted one time-step to the right:
First Series | x_{1} | x_{2} | ... | x_{n-1} |
Second Series | x_{2} | x_{3} | ... | x_{n} |
Here's another which
shows the difference between an uncorrelated signal and a signal exhibiting
strong autocorrelation.
Last Update: 2004-Jul-03