Bayesian Estimation And Application For Several Classes Of Mixture Double Autoregressive Models

Financial time series data exist widely in daily life,such as currency market and stock data,etc.The data has many characteristics,such as peak heavy-tailed,heteroscedasticity,fluctuation cluster,asymmetry and multi-peak.This kind of data is mainly modeled by generalized autoregression conditional heteroscedasticity model,which has a good performance in describing the heteroscedasticity of financial time series data,but can not accurately describe the characteristics of data such as peak heavy-tailed and multi-peak.Mixture time series model can approximate any distribution form,so it can model the data flexibly and effectively.Based on the double autoregressive model,this paper introduces the modeling idea of mixture model into it.Mixture double autoregressive model can better describe the properties of data such as peak heavy-tailed,multiple peaks and asymmetry,so it can describe financial time series data in a more precise way.This paper is divided into two parts.The first part considers the bayesian estimation problem of mixture double autoregression model,obtains the complete data likelihood of the model by introducing latent variables,and calculates the posterior distribution and full condition distribution of parameters according to bayesian theorem,so that MCMC sampling becomes feasible.Bayesian factor method was used to test the heteroscedasticity of the model.In the empirical study,the model is applied to the fitting problem of S&P500 stock daily return rate,and the results show that mixture double autoregressive model can describe such financial time series data well.A limitation of mixture double autoregressive model is that it can not describe the driving effect of explanatory variables on the model.In real life,the return rate of stocks is usually affected by other explanatory variables,leading to the random change of mixing probability.Therefore,on the basis of mixture double autoregressive model,explanatory variables are further introduced to extend the model to the logistic mixture double autoregressive model.This model can effectively describe the covariation-driven effect of financial time series data.The bayesian estimation problem of the logistic mixture double autoregressive model is systematically studied in the second part of this paper.The bayesian method is used to estimate the parameters of the model.In order to overcome the influence of the logistic function structure on the estimation,variable transformation is carried out.The simulation results show that the bayesian estimation based on variable transformation method can accurately estimate the model parameters,and the heteroscedasticity of the model is tested by the bayesian factor method.In the aspect of empirical study,the model is applied to the empirical analysis of Shanghai Composite Index,and the driving effect of two covariables,RMB/USD exchange rate and first-order lag of observed data,on the model is considered.The fitting results showed that the logistic mixture double autoregressive model could well describe the influence of external factors on financial time series data.