A discussion on the robust vector autoregressive models: novel evidence from safe haven assets

Abstract

The vector autoregressive (VAR) model has been popularly employed in operational practice to study multivariate time series. Despite its usefulness in providing associated metrics such as the impulse response function (IRF) and forecast error variance decomposition (FEVD), the traditional VAR model estimated via the usual ordinary least squares is vulnerable to outliers. To handle potential outliers in multivariate time series, this paper investigates two robust estimation methods of the VAR model, the reweighted multivariate least trimmed squares and the multivariate MM-estimation. The robust information criteria are also proposed to select the appropriate number of temporal lags. Via extensive simulation studies, we show that the robust VAR models lead to much more accurate estimates than the original VAR in the presence of outliers. Our empirical results include logged daily realized volatilities of six common safe haven assets: futures of gold, silver, Brent oil and West Texas Intermediate (WTI) oil and currencies of Swiss Francs and Japanese Yen. Our sample covers July 2017–June 2020, which includes the history-writing price drop of WTI on April 20, 2020. Our baseline results suggest that the traditional VAR model may significantly overestimate some parameters, as well as IRF and FEVD metrics. In contrast, robust VAR models provide more reliable results, the validity of which is verified via various approaches. Empirical implications based on robust estimates are further illustrated.