Arma Models With Arch Errors

Abstract. This paper considers the class of ARMA models with ARCH errors. Maximum Likelihood and Least Squares estimates of the parameters of the model and their covariance matrices are noted and incorporated into techniques for model building based upon the application of the usual Box‐Jenkins methodology of identification, estimation and diagnostic checking to the ARMA equation, the ARCH equation, and the full model. The techniques are applied to 16 U.S. macroeconomic time series and it is seen that in many of the series, models from this class can be constructed.