| Kim (1994) proposed State-Space Models with Markov Switching, a popular dynamic time series model. It regards unobserved and uncertain switching as a random variable which is endogenous and continuous. Markov switching model can be a good fit with the ongoing structural changes in the time series of variable data, and the model can solve the problem of structural mutations. State space model can combined component of observation data with that of unobserved data, and it can combine a lot of dynamic models of time series data into a unified structure. The form State space model is very flexible and many models can be represented it. For example, ARMA models, stochastic volatility models, unobserved-components time series model and time-varying parameters model. By using a strong iterative algorithm Kalman filter. The state space model can solve the time-varying coefficients and the existence of latent variable parameters (unobserved variables) effectively.State-Space Models with Markov Switching combine Markov switching model and the State space model into one, therefore, State-Space Models with Markov Switching can not only identify the time-varying parameters and latent variable parameters, but also depicts the changes in different states of the time series data and more complex dynamic evolution of that, thus, applying State-Space Models with Markov Switching into the macroeconomic and financial variables analysis is currently a hot research field.To some extent, State-Space Models with Markov Switching have made great success in the areas of macroeconomic and financial applications. For example, Kim and Nelson (1998a) use State-Space Models with Markov Switching to analyze the co-movement, relevance and duration dependence of the U.S. business cycle with macroeconomic data from January 1960 to January 1995, and elicit a new coincident index. Kim (1993) use State-Space Models with Markov Switching to analysis the inflation rate and inflation uncertainty with U.S. GNP deflator data from 1st quarter 1958 to 4th quarter 1990. The model can capture the shift of switching, while ARCH models and GARCH models can not do it. To some extent, State-Space Models with Markov Switching are superior to ARCH and GARCH model. However, the estimation of the model parameters is difficult, which leads to their application is still not widespread, compared to the general linear time series model. Especially, the research of State-Space Models with Markov Switching is more scarcely in our country. Therefore, this paper makes some innovative work in the modeling theory, algorithm derivation, the number of states and dimensions ascertain and the application of the models in our country macroeconomic business cycle fluctuation analysis.According to the main logic line of this research, this paper can be divided into six chapters, and there are as followings:Chapterâ… is an introduction part of this paper and discusses the background, purpose and meaning, content, the structure of the paper and the main innovation of this research.Chapterâ…¡introduces Markov switching model and the state space model, respectively, and discusses the definition, the derivation of the likelihood function, parameters estimation and quantitative analysis methods of the Markov switching model and the State space model in detail. Meanwhile, it introduces the several common forms of the state space model. This chapter lays the foundation for later chapters.Chapterâ…¢, firstly, we analyze the parameters estimation methods of State Space models with Markov Switching. Secondly, we apply this model to analyze the long term fluctuation of business cycle in our country. The results obtained are that China's business cycle has obvious asymmetric features before and after the reform and opening up, and macroeconomic expansion is much larger than the recession of economy. After 2000, the smoothed probability of China's business expansion has always been at the high level and the characteristics of the business cycle fluctuations is mainly the "high level-moderate flat" type. We divided our business cycle to the 10 round from 1952 to 2008 by the smoothed probability. Smooth probability reflects the features of our country business cycle, and provides a new way for dividing the business cycle. Chapter IV, first of all, we analyze the method of parameters estimation by using State Space models with Markov Switching and Gibbs Sampling. Secondly, This model is used to analysis the short-term fluctuations of our country business cycles, and focus on the co-movement and asymmetry of the business cycle with the data of total fixed assets investment, total retail sales, exports and employees on nonagricultural payrolls. The time period is 1992.1 through 2009.2. Result is that the co-movement of the business cycle fluctuations is obvious, while the Asymmetry is not obvious. Currently, our economy is still in recession, and turning point of the expand state is not appear. The business cycle fluctuations showed such characteristics to provide a reference to the macro-control policy-making of our government.Chapter V, we use EM algorithm and Monte Carlo simulation method to ascertain the number of states and dimensions of State Space models with Markov Switching. After that, it tests the number of states and dimensions of our business cycle. In the end, it comes to a conclusion that number of states are 2 and the dimensions are 3.Chapter VI is conclusion and prospects. We summarize the findings and put forward the prospects in future research.The innovations of this paper are as followings:Firstly, we point out the defects of AR, MA, ARMA models, ARCH and GARCH model in analysis of the business cycle. Meanwhile, it establishes the analysis framework of State Space models with Markov Switching, and research on modeling theory, algorithm and parameters estimation. it analyzes the long term fluctuations and short term fluctuations of the business cycle with China's macro-economic data. The results show that the model has a better estimation effect than the common linear model, ARCH and GARCH models, and this model is more practical value.Secondly, we put forward a new classification method of the business cycle. When analyzing the long term fluctuation of our business cycle, we get the smoothed probability. Further, China has gone through 10 rounds of the business cycle during 1952 and 2008 by the smoothed probability. This is consistent with our business cycle, and smoothed probability provides a new approach for division of business cycle. It is found that asymmetry is obvious in long term fluctuations of business cycle, while asymmetry is not obvious and co-movement is obvious in short term fluctuations. It is also found that the current state of our economy is still in recession, the turning point of expanding state does not occur.Thirdly, we determine the number of states and dimensions of the business cycle in our country. As usual, before the analysis of the business cycle, it is assumed to know the number of states of the business cycle. But this assumption is not reasonable. Under these conditions, there is no effective method to determine the number of states of the business cycle. This paper uses the EM algorithm and Monte Carlo simulation method to determine the number of the state of China's business cycle is 2 and the dimension is 3.
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