A score test for detecting extreme values in a vector autoregressive model

In this paper, we propose a score test to study a vector autoregressive model and its detection of extreme values. We take a likelihood approach to derive the corresponding maximum likelihood estimators and information matrix. We establish the score statistic for the vector autoregressive model under two perturbation schemes for identifying possible influential cases or outliers. The effectiveness of the proposed diagnostics is examined by a simulation study. To make an application, a data analysis is performed using the model to fit monthly log-returns of International Business Machines Corporation stock and the Standard & Poor's 500 index. Lastly, comparisons between the results by the score test and the local influence method are made. We establish two important findings that the score test is more effective while the local influence analysis can be used to diagnose more influential cases.