In this paper, we use a likelihood approach and the local influence method introduced by Cook [Assessment of local influence (with discussion). J Roy Statist Soc Ser B. 1986;48:133–149] to study a vector autoregressive (VAR) model. We present the maximum likelihood estimators and the information matrix. We establish the normal curvature and slope diagnostics for the VAR model under several perturbation schemes and use the Monte Carlo method to obtain benchmark values for determining the influence of directional diagnostics and possible influential observations. An empirical study using the VAR model to fit real data of monthly returns of IBM and SP500 index illustrates the effectiveness of our proposed diagnostics.
Liu, Y., Ji, G., & LIU, S. (2015). Influence diagnostics in a vector autoregressive model. Journal of Statistical Computation and Simulation, 85(13), 2632-2655. https://doi.org/10.1080/00949655.2014.967243