Open Access
February 2014 Nonparametric specification for non-stationary time series regression
Zhou Zhou
Bernoulli 20(1): 78-108 (February 2014). DOI: 10.3150/12-BEJ477


We investigate the behavior of the Generalized Likelihood Ratio Test (GLRT) (Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153–193]) for time varying coefficient models where the regressors and errors are non-stationary time series and can be cross correlated. It is found that the GLRT retains the minimax rate of local alternative detection under weak dependence and non-stationarity. However, in general, the Wilks phenomenon as well as the classic residual bootstrap are sensitive to either conditional heteroscedasticity of the errors, non-stationarity or temporal dependence. An averaged test is suggested to alleviate the sensitivity of the test to the choice of bandwidth and is shown to be more powerful than tests based on a single bandwidth. An alternative wild bootstrap method is proposed and shown to be consistent when making inference of time varying coefficient models for non-stationary time series.


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Zhou Zhou. "Nonparametric specification for non-stationary time series regression." Bernoulli 20 (1) 78 - 108, February 2014.


Published: February 2014
First available in Project Euclid: 22 January 2014

zbMATH: 06282543
MathSciNet: MR3160574
Digital Object Identifier: 10.3150/12-BEJ477

Keywords: conditional heteroscedasticity , functional linear models , generalized likelihood ratio tests , local linear regression , local stationarity , Weak dependence , wild bootstrap

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

Vol.20 • No. 1 • February 2014
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