The inverse partial correlation function of a time series and its applications

The concept of the inverse correlation function of a stationary process was introduced by Cleveland (Technometrics 14 (1972), 277-293). The inverse partial correlation function of a stationary process may intuitively be thought of as the corresponding extension of the concept of the partial correlation function. A precise mathematical definition of this function is given. Its importance in describing the structure of a moving average of finite order h is discussed. Having observed X1,...,XT, the autoregressive method of estimating the inverse correlations is employed for constructing sample estimates of the inverse partial correlations. For the hth-order moving average process, the estimates beyond h are, as T --> [infinity], asymptotically independent normally distributed with 0 mean and variance T-1. Their use for estimating h and for testing hypotheses concerning h is examined.