(Structural) VAR models with ignored changes in mean and volatility

The paper discusses how standard forecasting tools in multivariate time series analysis are affected when ignoring possible changes in the mean and the (co)variance. We study the estimation, forecasts, and estimated impulse responses of so-called long vector autoregressions, for which the complexity of the model increases with the sample size. We prove that, in spite of structural change in the data generating process, coefficient estimates and out-of-sample forecasts based on such long vector autoregressions are consistent. The sampling behaviour of estimated impulse responses depends primarily on the residual covariance matrix, which converges to an “average” covariance matrix in the case of varying (co)variances. Localised estimators (also obtained by means of a suitable long vector autoregression) may be more suitable in this case. Monte Carlo simulations support our theoretical findings. The empirical relevance of the theory is illustrated in two applications: (i) the international dynamics of inflation, and (ii) uncertainty and economic activity.