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Abstract

One of the well-known economic stylized facts is the time-varying and nonl inear features of macroeconomic time series models. Although parametric nonli near models are successful in fitting the data very well, the ability of outof- sample forecasting has been still unsatisfactory. For example, the widely used STAR model has the risk of model misspecification due to the fact that a strong functional assumption is imposed about how transition variables enter into the transition function. We propose a new semiparametric STAR model to improve the traditional one, which allows the transi-tion variables to enter i nto the transitransi-tion functransi-tion in a nonparametrically way. The new model can not only improve the ability of the out-of-sample prediction by mitigating the m isspecification risk, but also share the merit of good economic interpretatio n by preserving the structure of the traditional STAR model. We propose a new three-stage estimation method and establish the asymptotic properties of the proposed estimators. Using the monthly data of RMB effective exchange rates from January 1994 to July 2012, we compare our new model with other popular t ime series models including the random walk model, the AR models, the TAR mod el, the STAR model and the neural network model and find that our model has a significant advantage in out-of-sample prediction. And furthermore, to mot ivate the use of a time-varying model, we also pro-pose a new stability test. Comparing with existing test methods, our test can effectively detect not onl y sudden structural breaks but also smooth and continuous structural changes . Our paper provides not only theoretical and methodological contributions but also important applications in macroeconomic analysis and forecasts.

The research contributions of the paper are as follows:

Firstly, we first proposed semiparametric STAR model, estimate convert equation and the threshold method at the same time using three-stage estimation method, and give the asymptotic theory of the estimation method. Compared with existing STAR model, our model does not need any priori assumptions about fucntion form of transi-tion functransi-tion and can fit real data well.

Secondly, based on non-parameter estimation and wild bootstrap method, we pro-pose a new structure stability test. Compared with existing methods, this test requires less prior information and can effectively detect continuous structural changes.

Thirdly, we first test the stability of the bivariate relationship of Chinese main macroeconomic time series. This is not only the premise of correct selection of macro

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prediction model test, but also the premise of correctly using widely popular VAR mod-el and SVAR modmod-el, so it is an urgent need of fundamental research.

Lastly, using of Chinese macroeconomic data, we compare the main macroeco-nomic prediction models prediction effect, and comprehensive evaluate the applicabil-ity of the various models in Chinese macroeconomic forecast.

Key Words: STAR model; Semiparametric method; Stability test; Out-of-sample

forecast; Local linear estimation

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