Diagnostic analysis for a vector autoregressive model under Student's t-distributions

In this paper, we use the local influence method to study a vector autoregressive model under Student's t-distributions. We present the maximum likelihood estimators and the information matrix. We establish the normal curvature diagnostics for the vector autoregressive model under three usual perturbation schemes for identifying possible influential observations. The effectiveness of the proposed diagnostics is examined by a simulation study, followed by our data analysis using the model to fit the weekly log returns of Chevron stock and the Standard & Poor's 500 Index as an application.