On the use of the sample partial autocorrelation for order determination in a pure autoregressive process: a Monte Carlo study and empirical example

Sample partial autocorrelations are one of the main statistical tools of time series analysis. They are especially useful in identifying the order of an AR(p) process. In this note, we show via a simulation experiment that normalizing each sample partial autocorrelation with Anderson's (1993a) means and variances, instead of the large-sample moments, can yield asymptotic distributions that are better approximated by the N(0,1) distribution. The important implication of this result is that the true order of a pure autoregressive process can be incorrectly identified due to use of the large-sample mean and variance of sample partial autocorrelations. An empirical example given in Box and Jenkins (1976) is used to highlight this problem.