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Threshold autoregressive model financial time series analysis and econometrics , an important class of nonlinear time series model by Dr. Tang Jiahao (H.Tong) in 1978 proposed threshold autoregressive model built on a smooth time traversing the the nature , Caner and Hansen (2001) , originality of the threshold model with a unit root , this article is in its foundation to study the statistical inference of the progressive nature of the three sections of the threshold model , enrich and develop the non-linear model in study time series nonstationary theory , has important theoretical significance and realistic significance . First, this paper systematically introduce the threshold since the regression model of the origin and development process , the threshold since the basis of the regression model , is proposed dual- threshold autoregressive model dual - threshold model the problem of dealing with periodic financial time series , the apparent advantages : the model can reflect the location of the economic growth ( accelerated growth , general growth ), recession ( recession accelerated , general recession) , or shock period . Secondly, this study door threshold regression model with unit root null hypothesis H0 Theorem 1 , the last article in Appendix given in this article used Lemma 1 , Lemma 2 and the lead proof of Lemma 3 . innovation of this paper are: 1, the system introduces the definition of the threshold model , threshold autoregressive model in the economic , financial , astronomical , population dynamics ; 2 , the proposed dual - threshold model realistic background , which gives the definition of dual- threshold model , model parameter estimation and model identification ; 3 , with unit root door only from the regression model , the joint hypothesis H 0 < / sub > : θ under 1 = θ 2 = θ 3 , the asymptotic distribution of the statistic W T 4 to discuss W < sub> T bootstrap asymptotic distribution of the two approximate methods , one is based on unlimited , another unit root is imposed restrictions thus calculated by these approximate distribution of the critical value and p- value.
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