A Generalization of Partial Autocorrelations Useful in Identifying ARMA Models

Statistics are proposed to help identify the orders of autoregressive-moving average models. These are functions of the sample autocorrelations and include partial autocorrelations as special cases. The large-sample variances of the statistics are derived and small-sample properties are explored by simulation. Their interpretation is illustrated using Wolfer's annual sunspot numbers and wind velocity data (Cleveland 1972).