Application Of Approximate Bayesian Computing In Parameter Estimation Of AR Model

Time series analysis is an important branch of statistics,which mainly studies the process of the occurrence and development of things with the change of time,and seeks for the laws of the development and change of things and predicts the future trend.AR model in time series analysis is a kind of important statistical model.This model is widely used in financial,economic,biological,social,and other fields.The parameter estimation of the model is the most important link in time series research.The method of parameter estimation in statistical is systematic,has a solid theoretical foundation,but also more complex,has a higher request to the data characteristics.Common parameter estimation methods: torque estimation method,the least squares estimation method,minimum variance estimation method,maximum likelihood estimation method,the method to estimate the maximum office,etc.But these methods deriving process is more complex.Under the condition of guarantee of accuracy and selection Efficient estimation method is a hot spot in the parameter estimation of.Many literatures in recent years,respectively from the Angle of theory and practice,has made great progress.Approximate bayesian calculation(shorthand for ABC)is a popular in recent years based on bayesian statistical method of parameter estimation.Compared with the maximum likelihood estimation,this method is significantly characteristics is to replace the likelihood function with the method of the simulation calculation.Especially for complex model estimation,this method has obvious advantages.In this paper,approximate bayesian calculation method was used to study the AR model parameter estimation.First,we discussed the white noise as gaussian distribution ABC of AR model parameter estimation.The ABC method is essentially refused to algorithm,the most important link is as far as possible choose low dimensional parameters information more statistics,so that we can reduce the probability of rejection,improve the efficiency of the algorithm.This paper chose the autocorrelation coefficient as parameters,to simulate the statistic from the estimated results,this method is better than maximum likelihood estimation method.Considering the white noise in the financial model usually obey the heavy-tailed,white noise obey the generalized error is discussed AR model parameters are estimated ABC.In addition this paper also discusses the ABC parameters estimation of generalized error distribution.At the end of the paper to collect data in recent years,the Shenzhen index of Shenzhen stock index respectively set up white noise is normal distribution and generalized error distribution of AR model,using the ABC algorithm to estimate model parameters from the results,white noise obeys general distribution of AR model is more reasonable.