Abstract
Time series analysis is a tremendous research area in statistics and econometrics. As remarked in a review by Howell Tong in 2001, for about 100 years up to 2001 Biometrika (alone) published over 400 papers on the subject. [Tong (2001)] Furthermore, in the review, Howell Tong is able break down up to fifteen key areas of research interest in time series analysis. Nonetheless, unlike that of Howell Tong, the aim of the review in this paper is not to cover a wide range of topics on the subject, but is to concentrate on a small, but extremely essential, point he made on the semiparametric methods in nonlinear time series analysis and to explore into various aspects of this research area in much more details. It is also an objective of this review to provide some discussion on a future research where appropriate.
Highlights
In time series regression, nonparametric methods have been very popular both for prediction and characterizing nonlinear dependence
We have seen in literature that theoretical and empirical research in time series analysis may be conducted within a large number of topics
In order to take into account the nonlinearity in time series regression, nonparametric methods have been very popular both for prediction and characterising nonlinear dependence
Summary
Nonparametric methods have been very popular both for prediction and characterizing nonlinear dependence. The review concentrates on existing works on the consistency of nonparametric estimators with some key studies such as Wang and Phillips (2009a); Wang and Phillips (2009b); Karlsen and Tjostheim (2001); Karlsen et al (2007); Karlsen et al (2010) It is the discussion on semiparametric models and model specification tests with stationary data; see Gao et al (2009a); Gao et al (2009b); Gao and King (2012); Gao et al (2012b) for some recent studies related to hypothesis testing of nonstationarity which are not yet available in Sun and Li (2012).
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