A Higher-order Markov-switching Autoregression Model With Its Application

In the economic field,the staggered effects of many factors make the structure of time series data a large extent change.In order to ensure the accuracy of the time series,the research scholars at home and abroad put forward many switching models,and the Markov switching model is one of the more popular.In addition,taking into account the autocorrelation of the time series,scholars have proposed different high-order switching models.Since the high-order Markov chain can describe properly the characteristics of time series,this paper introduces the high-order Markov chain into the general Markovian autoregressive model,and proposes a high-order markov-switching autoregression model.And the paper uses the ‘collapsed' from of the transition probability matrix to realize the low order expression of the higher order model.Finally,a likelihood function is established based on the normal hypothesis of the time series' distribution,and the parameters estimation of higher order model is realized by maximum likelihood estimation.In the case study,this paper applies the high order Markov switching autoregressive model to analyses fluctuations of the weekly closing price of the Shanghai Composite Index.Before analyzing the volatility,this paper deals with the closing price and transforms it into the weekly yield rate series,which reflects the fluctuation of the weekly closing price through the fluctuation of the weekly yield rate series.And the numerical results show it can identify the range of periodic fluctuations of return series conveniently,and depict tiny characteristic of fluctuations effectively,To deal with the time series and establish the actual modeling is the key to analyze the volatility of the time series.The concrete operation is as follows:Firstly,in order to better analyze the volatility of the time series,this paper chooses a weekly closing price,which can avoid insufficient sample and stock volatility caused by short impact.Before analyzing the fluctuation of the weekly closing price,this paper transforms the time series into the weekly yield rate time series reflecting the fluctuation of the weekly closing price.Secondly,using the markov-switching autoregression model must ensure the non-stationary of the time series,that is,the sequence must be nonlinear and structural transformation.In this paper,we must ensure that there are a non-linear and structural change in the SSE Composite Index weekly return rate time series.This paper uses the corresponding R functions to verify the nonlinearity of time series and the structural transformation.Finally,the order of the autoregressive model is determined by using the AIC criterion before establishing the actual high-order markov-switching model.The likelihood function is established based on the time series' distribution being normal distribution.The parameters estimation of the higher order model is realized.Finally,this paper makes a volatility analysis for the Shanghai Composite Index weekly return rate time series.