Robust modelling of periodic vector autoregressive time series

This paper develops a robust estimation and identification method for periodic vector autoregressive models (hereafter PVAR) with linear constraints set on parameters for a given season. Since the least squares estimators are extremely sensitive to additive outliers, this paper suggests a robust estimation based on residual autocovariances (RA) and analyses the asymptotic properties of these RA estimates. To identify the optimal order of the PVAR, this paper also uses a genetic algorithm with Bayes information criterion (BIC). The proposed procedure is applied to a small simulation study for PVAR models in the case of four seasons. Empirical results show that the robust estimators perform better than the least squares estimators when the contamination rate of the additive outliers is at random or at fixed positions.