## Bernoulli

- Bernoulli
- Volume 20, Number 1 (2014), 78-108.

### Nonparametric specification for non-stationary time series regression

#### Abstract

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.

#### Article information

**Source**

Bernoulli, Volume 20, Number 1 (2014), 78-108.

**Dates**

First available in Project Euclid: 22 January 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.bj/1390407281

**Digital Object Identifier**

doi:10.3150/12-BEJ477

**Mathematical Reviews number (MathSciNet)**

MR3160574

**Zentralblatt MATH identifier**

06282543

**Keywords**

conditional heteroscedasticity functional linear models generalized likelihood ratio tests local linear regression local stationarity weak dependence wild bootstrap

#### Citation

Zhou, Zhou. Nonparametric specification for non-stationary time series regression. Bernoulli 20 (2014), no. 1, 78--108. doi:10.3150/12-BEJ477. https://projecteuclid.org/euclid.bj/1390407281