A model-adaptive test for parametric single-index time series models. (English) Zbl 1416.62533

Xia, Qiang; He, Kejun; Niu, Cuizhen

J. Time Ser. Anal. 38, No. 6, 981-999 (2017).

Summary: In this paper, based on certain residual-marked empirical processes, we study the model test to validate the composite structure with a given link function for parametric single-index time series models. To extend an existing directional test that avoids the curse of dimensionality to an omnibus test, a model-adaptive dimension-reduction test procedure is proposed. Moreover, to fully utilize the dimension-reduction structure under the null hypothesis, the test is designed for adapting both the null and alternative hypotheses, which can improve the power for a more general alternative. Simulation results and a real data example show that the proposed method can perform effectively in checking parametric single-index time series models.

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F03	Parametric hypothesis testing

Keywords:

residual-marked empirical process; dimension reduction; globally smoothing