A New Look at Portmanteau Tests
- 79 Downloads
Portmanteau tests are some of the most commonly used statistical methods for model diagnostics. They can be applied in model checking either in the time series or in the regression context. The present paper proposes a portmanteau-type test, based on a sort of likelihood ratio statistic, useful to test general parametric hypotheses inherent to statistical models, which includes the classical portmanteau tests as special cases. Sufficient conditions for the statistic to be asymptotically chi-square distributed are elucidated in terms of the Fisher information matrix, and the results have very clear implications for the relationships between the parameter of interest and nuisance parameter. In addition, the power of the test is investigated when local alternative hypotheses are considered. Some interesting applications of the proposed test to various problems are illustrated, such as serial correlation tests where the proposed test is shown to be asymptotically equivalent to classical tests. Since portmanteau tests are widely used in many fields, it appears essential to elucidate the fundamental mechanism in a unified view.
Keywords and phrases.Portmanteau test Asymptotic local power Serial correlation Time series analysis Variable selection
AMS (2000) subject classification.62F03 62F05
Unable to display preview. Download preview PDF.
Authors thank the Associate Editor and an anonymous Referee for their constructive comments on an earlier version of the paper. The third author thanks the Research Institute for Science & Engineering, Waseda University, for their supports.
- Brillinger, D.R. (1981). Time Series: Data Analysis and Theory, Vol. 36 SIAM.Google Scholar
- Durbin, J. (1970). Testing for serial correlation in least-squares regression when some of the regressors are lagged dependent variables. Econometrica pp. 410–421.Google Scholar
- Godfrey, L.G. (1976). Testing for serial correlation in dynamic simultaneous equation models. Econometrica pp. 1077–1084.Google Scholar
- Li, W.K. (2003). Diagnostic checks in time series. Chapman and Hall.Google Scholar
- Rao, C.R. (1973). Linear statistical inference and its applications. Wiley Series in Probability and Mathematical Statistics (EUA).Google Scholar