Identification of Dynamic Regression (Distributed Lag) Models Connecting Two Time Series

A methodology is introduced for identifying dynamic regression or distributed lag models relating two time series. First, specification of a bivariate time-series model is discussed, and its relationship to the usual dynamic regression model is indicated. Then, a two-stage identification procedure is presented which involves fitting univariate time-series models to each series, and identifying a dynamic shock model relating the two univariate model innovation series. The models obtained at these two stages are combined to identify a dynamic regression model, which may then be fitted in the usual ways. Two systems of economic time series illustrate the methodology.