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,

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... t 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 aspect of this research area in much more detail. It is also an objective of this review to provide some discussion on a future research where appropriate.