Automatic Specification Testing for Vector Autoregressions and Multivariate Nonlinear Time Series Models

This article introduces an automatic test for the correct specification of a vector autoregression (VAR) model. The proposed test statistic is a Portmanteau statistic with an automatic selection of the order of the residual serial correlation tested. The test presents several attractive characteristics: simplicity, robustness, and high power in finite samples. The test is simple to implement since the researcher does not need to specify the order of the autocorrelation tested and the proposed critical values are simple to approximate, without resorting to bootstrap procedures. In addition, the test is robust to the presence of conditional heteroscedasticity of unknown form and accounts for estimation uncertainty without requiring the computation of large-dimensional inverses of near-to-singularity covariance matrices. The basic methodology is extended to general nonlinear multivariate time series models. Simulations show that the proposed test presents higher power than the existing ones for models commonly employed in empirical macroeconomics and empirical finance. Finally, the test is applied to the classical bivariate VAR model for GNP (gross national product) and unemployment of Blanchard and Quah (1989 Blanchard, O. and Quah, D. 1989. “The Dynamic Effects of Aggregate Demand and Supply Disturbances,”. The American Economic Review, 79: 655–673. Web of Science ®] , Google Scholar]) and Evans (1989 Evans, G. W. 1989. “Output and Unemployment Dynamics in the United States: 1950–1985,”. Journal of Applied Econometrics, 4: 213–238. Crossref], Web of Science ®] , Google Scholar]). Online supplementary material includes proofs and additional details.