Model-based asymptotic inference on the effect of infrequent large shocks on cointegrated variables

Quasi-maximum-likelihood (QML) estimation of a model combining cointegration in the conditional mean and rare large shocks (outliers) with a factor structure in the innovations is studied. The goal is not only to robustify inference on the conditional-mean parameters, but also to find regularities and conduct inference on the instantaneous and long-run effect of the large shocks. Given the cointegration rank and the factor order, χ²${\chi }^2$ asymptotic inference is obtained for the cointegration vectors, the short-run parameters, and the direction of each column of both the factor loading matrix and the matrix of long-run impacts of the large shocks. Large shocks, whose location is assumed unknown a priori, can be detected and classified consistently into the factor components.