Bayesian Subset Selection For Double Threshold Moving Average Models

With the continuous development of the data age,the nonlinear time series model has gradually developed.For many economic data,such as the IBM stock market price and the weekly spot exchange rate of the pound,the nonlinear time series model can accurately describe the characteristics of its behavior.In the exchange rate analysis of the yen against the US dollar,Xia et al.(2010)established a single-threshold two-mechanism MA model,with the reversible jump Monte Carlo method,not only the threshold effect can be tested,but also the parameter values in the model is estimated.However,in the actual analysis,the number of thresholds is not unique,and it is necessary to consider the model of double threshold or even multiple thresholds.Therefore,this paper proposes a double-threshold moving average(DTMA)model,which can handle data analysis in complex situations well,but there are more parameters to be considered,and the estimation problem of the model becomes complicated.In frequency statistical analysis,it is very challenging.Bayesian statistics can avoid complex high-dimensional integrals,and the MCMC sampling method can effectively solve the parameter estimation problem of the model.This paper will start to study the Bayesian optimal subset selection problem of DTMA model.For the selection of the optimal subset of the double threshold moving average model(DTMA),the Bayesian method is first applied to the parameter estimation of the model,combined with random search variable selection(SSVs)method to select the optimal subset of the double threshold moving average(DTMA)model.Then the actual problem is analyzed according to the Bayesian optimal subset selection method of DTMA model.By discussing the selection of the prior distribution of DTMA model parameters,the Bayesian theorem is used to derive the posterior distribution of the parameters.According to the posterior distribution results of DTMA model parameters,the MCMC sampling scheme for model parameter estimation is given.In the MCMC algorithm,we will combine the Gibbs sampling and the Metropolis-Hastings(MH)algorithm.Under the idea of the random search variable selection(SSVS)method,not only the optimal subset of the model can be selected,but also the MCMC sampling method can simultaneously estimate.The values of the threshold variable and the delay parameter are included in the model.Simulation experiments show that the Bayesian optimal subset selection method verifies the accuracy and validity of parameter estimation and optimal subset model selection,despite the large number of subsets,and the uncertain of threshold parameters and delay variables.Finally,the double threshold moving average model is used for empirical analysis.The actual data was selected from the Japanese yen to US dollar exchange rate data from January 1986 to December 2018 as the research object,we can establishes the exchange rate data model and distinguish the best subset models successfully.Compared with the single-threshold MA model,the AIC value shows that the model in this paper is better,indicating that the doublethreshold or multi-threshold performs better in the actual application analysis.