Robust Multivariate Observation-Driven Filtering for a Common Stochastic Trend: Theory and Application

We introduce a nonlinear semi-parametric model that allows for the robust filtering of a common stochastic trend in a multivariate system of cointegrated time series. The observation-driven stochastic trend can be specified using flexible updating mechanisms. The model provides a general approach to obtain an outlier-robust trend-cycle decomposition in a cointegrated multivariate process. A simple two-stage procedure for the estimation of the parameters of the model is proposed. In the first stage, the loadings of the common trend are estimated via ordinary least squares. In the second stage, the other parameters are estimated via Gaussian quasi-maximum likelihood. We formally derive the theory for the consistency of the estimators in both stages and show that the observation-driven stochastic trend can also be consistently estimated. A simulation study illustrates how such robust methodology can enhance the filtering accuracy of the trend compared to a linear approach as considered in previous literature. The practical relevance of the method is shown by means of an application to spot prices of oil-related commodities.