The Asymptotic Distribution of the Sample Autocorrelations for an Integrated ARMA Process

Abstract

The behavior of the sample autocorrelation function, r(k), for an integrated autoregressive moving average time series is examined. The nonnormal asymptotic distribution of r(k) is characterized as a function of lag k and the parameters of the process. The validity of the approximation in moderate-sized samples is examined.

Key Words:

• Time series analysis
• Nonstationarity
• Sample autocorrelation function