Distributions of the Sample Autocorrelations When Observations Are From a Stationary Autoregressive-Moving-Average Process

Abstract

This article examines the adequacy of approximations to the distributions of the sample autocorrelations by normal distributions, Edgeworth-type expansions, and four-parameter Pearson distributions. The accuracy of these approximations is found to depend critically on the data-generating process and sample size and to improve with sample size. Only the Pearson approximations seem to be reliable in relatively small samples. The utility of these approximations is illustrated with applications. A major obstacle to using these approximations is the necessity of obtaining the exact moments of the sample autocorrelations. Convenient expressions are developed from which the moments can be computed rather easily.

KEY WORDS:

• Approximating distributions
• Edgeworth expansion
• Model identification
• Pearson distributions
• Sample autocorrelations