Groupe d’études et de recherche en analyse des décisions

# On Robust Forecasting in Dynamic Vector Time Series Models

## Christian Gagné et Pierre Duchesne

In this article, robust estimation and prediction in multivariate autoregressive models with exogenous variables (VARX) are considered. The conditional least squares estimators (CLS) are known to be non robust when outliers occur. To obtain robust estimators, the method introduced in Duchesne (2005) and Bou Hamad and Duchesne (2005) is generalized for VARX models. The asymptotic distribution of the new estimators is studied and from this is obtained in particular the asymptotic covariance matrix of the robust estimators. Classical conditional prediction intervals normally rely on estimators such as the usual non robust CLS estimators. In the presence of outliers, such as additive outliers, these classical predictions can be severely biased. More generally, the occurrence of outliers may invalidate the usual conditional prediction intervals. Consequently, the new robust methodology is used to develop robust conditional prediction intervals which take into account parameter estimation uncertainty. In a simulation study, we investigate the finite sample properties of the robust prediction intervals under several scenarios for the occurrence of the outliers, and the new intervals are compared to non-robust intervals based on classical CLS estimators.

, 39 pages