This technique depends on the Yule-Walker equations . The mixed autoregressive-moving average model adds flexibility. The backshift operator B acts on a whole process at once. These equations may be inverted. X , an infinite-order autoregression.
All stationary ARs are invertible.
From now on we shall always deal with the invertible version. Parameter estimation routines produce invertible estimated time series. The sample ACF is r k , calculated from the sample autocovariance function c k . And remember that the ACF is only defined for stationary Time Series, so don't use the SACF of a clearly non-stationary data set. The correlogram is a plot of r k against k .