Multivariate Autoregressive Time Series Using SchweppeWeighted Wilcoxon Estimates

The vector autoregressive model in multivariate time series analysis is commonly used across different fields due to its simplicity in application. The traditional method for estimating the model parameters is the least squares minimization. However, since least squares estimates are sensitive to outliers, more robust techniques have become of interest. This paper investigates a robust alternative by obtaining the estimates using a weighted Wilcoxon dispersion with Schweppe weights. Under the so-called innovations outlier model where outliers are introduced through the error distribution, the proposed estimator is shown to be asymptotically multivariate normal, centered about the true model parameters, at a rate of n(-1/2). In addition, a Monte Carlo study is presented to evaluate the performance of various estimators. The study results suggest that the Schweppe-weighted Wilcoxon estimates will generally have best performance. This result is most noticeable under the presence of additive outliers or when the series is closer to non-stationarity.