Parameter Estimation And Application Of ARMA Model Based On Hybrid Algorithm

ARMA model is widely used in time series analysis,and its parameter estimation plays an important role.At present,scholars have put forward many estimation methods,but there are many problems,such as the large amount of computation,slow convergence speed or low accuracy.Therefore,finding a simpler method to get accurate estimation will be very helpful for the follow-up research work.To solve the above problems,this paper mainly uses the Approximate Bayesian Computation(ABC)method and EM algorithm to estimate the parameters of ARMA model,and are used to analyze and solve practical problems.According to the properties of autocorrelation function of ARMA model,study the model coefficients and white noise separately: when estimating the coefficients of ARMA model,firstly,the sample autocorrelation function is used as the statistic to estimate the AR coefficients,then the ARMA model is transformed into the MA model and estimate the MA coefficients,the accuracy of ABC algorithm is verified by numerical simulation comparing with the maximum likelihood estimation.When estimating the white noise parameters of ARMA model,the ABC estimation of white noise is normal distribution and mixed normal distribution are given respectively,and the EM estimation is performed for white noise parameters is mixed normal distribution,numerical simulation shows that the EM algorithm is more accurate than the ABC algorithm when white noise is mixed normal distribution.for ARMA model with white noise is normal distribution,ABC algorithm is used for parameter estimation;for ARMA model with white noise is mixed normal distribution,ABC-EM hybrid algorithm is the more effective method for parameter estimation.The innovation of this paper is that when ABC algorithm is used to estimate the parameters of ARMA model,the sample autocorrelation function of ARMA model is used as the statistic to estimate the parameters of AR coefficient,MA coefficient and white noise respectively.This layering idea is very practical especially in the highorder models,by reducing the parameters and simplifying the calculation steps,the calculation cost is greatly reduced.For ARMA model with white noise is mixed normal distribution,the hybrid algorithm proposed in this paper absorbs the advantages of multiple methods and breaks the limitations of a single algorithm,not only reduces the complexity of calculation,but also improves the accuracy of estimation.