Autocorrelation Function
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See: Function, AFC, Autocorrelation Analysis, Autocorrelation Coefficient, Partial Autocorrelation Function.
References
2011
- http://en.wikipedia.org/wiki/Autocorrelation#Statistics
- QUOTE: In statistics, the autocorrelation of a random process describes the correlation between values of the process at different points in time, as an function of the two times or of the time difference. Let X be some repeatable process, and i be some point in time after the start of that process. (i may be an integer for a discrete-time process or a real number for a continuous-time process.) Then Xi is the value (or realization) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μi and variance σi2 for all times i. Then the definition of the autocorrelation between times s and t is: [math]\displaystyle{ R(s,t) = \frac{\operatorname{E}[(X_t - \mu_t)(X_s - \mu_s)]}{\sigma_t\sigma_s}\,,
}[/math] where "E" is the expected value operator. …
… When the autocorrelation function is normalized by mean and variance, it is sometimes referred to as the 'autocorrelation coefficient.
- QUOTE: In statistics, the autocorrelation of a random process describes the correlation between values of the process at different points in time, as an function of the two times or of the time difference. Let X be some repeatable process, and i be some point in time after the start of that process. (i may be an integer for a discrete-time process or a real number for a continuous-time process.) Then Xi is the value (or realization) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μi and variance σi2 for all times i. Then the definition of the autocorrelation between times s and t is: [math]\displaystyle{ R(s,t) = \frac{\operatorname{E}[(X_t - \mu_t)(X_s - \mu_s)]}{\sigma_t\sigma_s}\,,
}[/math] where "E" is the expected value operator. …