The k-th order autocorrelation (ACFk) of time series X is the measure of closeness and direction of linear stochastic dependency between the current values of a time series and values of the time series k time moments ago. In other words, autocorrelation is a "pure" correlation between Xt and Xt-k.
The partial k-th order autocorrelation (PACFk) of time series is the measure of closeness and direction of linear stochastic dependency between the current values of a time series and values of the time series k time moments ago, excluding influence of intermediate values Xt-1, Xt-2, …, Xt-k+1.
Suppose that X is the original time series, and T is the length of the time series.
Standard error:
Autocorrelation function (ACF):
t = 1... lag.
Partial autocorrelation function (PACF):
t = 1... lag.
Q-statistics:
t = 1...lag.
See also:
| ISmAutoCorrelation | SmAutoCorrelation | ISmPartialCorrelation | Modeling and Forecasting: ACF and PACF