On subset least squares estimation and prediction in vector autoregressive models with exogenous variables

Abstract We establish the consistency and the asymptotic distribution of the least squares estimators of the coefficients of a subset vector autoregressive process with exogenous variables (VARX). Using a martingale central limit theorem, we derive the asymptotic normal distribution of the estimators. Diagnostic checking is discussed using kernel‐based spectral density estimators. Multi‐step conditional prediction intervals are developed. In a small empirical study, subset VARX models are fitted and compared when lags are chosen according to some popular model selection techniques. Coverage properties of the prediction intervals are illustrated. An application to the monthly production of cheese in Canada for the time period 2003–2021 illustrates the methodology.