ARIMA Processes With ARIMA Parameters

This article introduces a general class of nonlinear and nonstationary time series models whose basic scheme is an autoregressive integrated moving average (ARIMA). The main feature is that the parameters are assumed to behave like a vector ARIMAx model in which the exogenous (x) component is represented by the regressors of the observable process. For this class a general algorithm of identification-estimation is outlined, based on the sampling information alone. The initial estimation, in particular, consists of an iterative procedure of nonlinear regressions on recursive parameter estimates generated with the extended Kalman filter. An empirical example on real economic data illustrates the method and compares alternative criteria of estimation