ACF and PACF
We have the time series Yt 1 < t < T which may be conceptualized as a stochastic process Y observed at times 1 < t < T. If a process is observed at successive times, it is also plausible that the process value at time t depends on the process values at time t-1, t-2, .... The specification of the dependency is the crux of time series modeling. As in the regression models, we have the error process in εt, 1 < t < T which is generally assumed to be white-noise process. Now, the process/time series Yt 1 < t < T may depend on its own past values, or on the past error terms. The two measures/metrics useful in understanding the nature of dependency are the Autocorrelation function (ACF) and Partial-autocorrelation function (PACF). We need the lag concept first though. For the process Yt 2 < t < T the lag 1 process is Yt-1, 1 < t < T - 1 . In general, for the variable Yt the k-th lag variable is Yt-k. The lag k ACF is defined as the correlation between...
