Research And Application Of Time-series VARFIMA Model

Recent years have witnessed wide applications of time series analysis in many fields. Particularly in the economic field, more and more practitioners have given intensive research to time series analysis methods to make full use of them. With the deepening of reform and the rapid development of economy, there is a large need for data analysis and processing in the economic field of China. However, in practical applications, due to the particularity of the economic field, the use of frequency often encounter many difficulties in traditional statistical methods for economic time series model analysis. Therefore, this thesis introduces a new model for economic time series analysis of a Bayesian analysis. Bayesian analysis methods provide a more rational analytical framework for economic time series models.The Bayesian inference theory and applications of the vector autoregressive moving average model (VARMA) and the whole sub-vector autoregressive moving average model (VARFIMA) are mainly studied.Firstly, a time series VARMA model with Bayesian methods is studied. Then the statistical structure of the model and its likelihood function are analyzed, according to the likelihood function the prior distribution of model parameters is constructed. The normal-Gamma prior distribution of Bayesian inference is studied. On the basis of the theory derived from statistical methods the distribution of the forecast is predicted. A set of two-dimensional time series simulated by MATLAB is uitilized, and the WinBUGS is used to the simulation analysis of VARMA model.Secondly, a multi-variable model of long memory time series VARFIMA Bayesian analysis is studied. On the basis of the analysis of VARFIMA (p, d, q) model of the statistical structure, the model likelihood function and parameters of the prior distribution are constructed, and then the conditions posterior distribution density function of the model parameters are derived with high precision. A set of two-dimensional time series simulated by MATLAB is utilized, and the WinBUGS is used to the simulation analysis of VARFIMA model.