## Nonparametric specification for non-stationary time series regression.(English)Zbl 1400.62205

Summary: We investigate the behavior of the generalized likelihood ratio test (GLRT) [J. Fan et al., Ann. Stat. 29, No. 1, 153–193 (2001; Zbl 1029.62042)] 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.

### MSC:

 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62G10 Nonparametric hypothesis testing 62G08 Nonparametric regression and quantile regression 62G09 Nonparametric statistical resampling methods

Zbl 1029.62042

fda (R)
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### References:

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