Distribution of the Residual Cross-Correlation in Univariate ARMA Time Series Models

Abstract

Cross-correlations between univariate autoregressive moving average (ARMA) time series residuals are useful in the examination of relationships between time series (Pierce 1977a) and in the identification of dynamic regression models (Haugh and Box 1977). In this article, the asymptotic distribution of these residual cross-correlations is derived, and its application to the problem of testing for lagged relationships in the presence of instantaneous causality is discussed. Some results of a simulation study to investigate the accuracy of the asymptotic variances and covariances of the residual cross-correlations in finite samples are reported.

Key Words:

• ARMA time series
• Granger causality
• Model identification
• Relationships between time series
• Residual cross-correlations