A Flexible Nonlinear Time Series Model And Its Application

In economics, the relationship between variables is often nonlinear, not linear. Thus, the traditional linear model is not suitable when describing the relationship between economic variables. In order to describe the relationship between economic variables more accurately, many non-linear models have been proposed. Compared with the linear model, these nonlinear models take into account the structural changes of relationship between economic variables. Thus, these models can describe the relationship more accurately. However, when setting these non-linear models, the evolution of structural changes of parameters is required to be set artificially. It will lead to the new problem of model misspecification. In order to reduce model misspecification in nonlinear model caused by the human factor, there is an urgent need to develop a flexible nonlinear model. Such flexible nonlinear models should reduce the subjectivity and arbitrariness to the maximum when setting models and can accommodate a variety of emerging nonlinear models.In this paper, we describe two flexible nonlinear time series model in the framework of state space model, a single equation flexible nonlinear time series model and a flexible VAR model. The two flexible nonlinear time series model parameters do not need to make any human assumptions on the law of parameters'evolution, but adhering to the econometrics, "Let the data speak', estimate the law of evolution from the data. This reduce the model misspecification existed in the common nonlinear model greatly. On the other hand, our model can accommodate all kinds of common nonlinear time series model. When the model parameters take different values, it can be converted to a variety of common nonlinear time series model. Single equation flexible nonlinear time series model is developed from the traditional time-varying parameter model (TVP). By introducing distance function and sorting, the time-varying parameter model can be converted to a single equation flexible nonlinear time series model. Flexible VAR model is developed from traditional VAR model. Single equation flexible nonlinear time series model and flexible vector autoregressive model are estimated by Markov chain Monte Carlo method (MCMC). MCMC method uses high-speed computing performance of modern computers and can estimate the parameters of the model feasibly and effectively.The flexible nonlinear model takes a big step from the nonlinear model and has profound developmental value and applied foreground. It has been regarded adequately and developed rapidly in abroad. But in China, the research on flexible nonlinear model is still seldom and just in the period of beginning. We use the flexible nonlinear model to study several problems of the macroeconomic field. The main contribution of our paper can be expressed in the following:(1) the innovation of econometric model and estimation method. Among the empirical researches in China, most of the models are linear model and common nonlinear model. The model in our paper has great flexibility. It can accommodate linear model and all nonlinear models and it is unnecessary to specify the evolutive mechanism. Our estimation method is MCMC method. In the flexible nonlinear model, it is impossible to use OLS and ML method to estimate the parameters. But MCMC method can make full use of the rapid computational character of computer and make feasible and effective estimation. Therefore our econometric model and estimation method make great contribution to improve domestic econometric model and have significant value on econometric method. (2) the innovation of visual angle in research. Among the literature of studying the sensitivity of credit demand on interest, most of the econometric models are linear model. This paper first uses the flexible nonlinear model to study the problem. The result shows that the sensitivity of credit demand on interest is changing companied by the different speed of economic growth. Among the literature of studying the effect of monetary policy, most of them use traditional VAR model. This paper uses flexible VAR model to study the effect of monetary policy. The result shows that the effect of monetary policy on economy has the significant time varying feature. (3) the conclusion of our research has great value for economics and policy. The result shows that when the speed of economic growth is vey high or very low, credit demand is not sensitive to interest. Only when the speed is medium, credit demand is sensitive to interest. It means that the effect of using interest tool to control economic cycle is still very limited. In the analysis of our monetary policy on, it can be found that monetary policy has bigger effect on economic growth rate and inflation rate in the earlier time. However, in recent years, the effect of monetary policy on economic growth and inflation become weaker. It means that we still need to improve the conductive channel of monetary policy to improve the effect of monetary policy. All the above finds are based on the flexible nonlinear model. From this point, this paper has significant value for academic and application.