  In this paper, the parameter estimation of ARMA(p,q) model is given by
approximate Bayesian computation algorithm. In order to improve the sampling
efficiency of the algorithm, approximate Bayesian computation should select as
many statistics as possible with parameter information in low dimension.
Firstly, we use the autocorrelation coefficient of the first p+q order sample
as the statistic and obtain an approximate Bayesian estimation of the AR
coefficient, transforming the ARMA(p,q) model into the MA(q) model. Considering
the first q order sample autocorrelation functions and sample variance as the
statistics, the approximate Bayesian estimation of MA coefficient and white
noise variances can be given. The method mentioned above is more accurate and
powerful than the maximum likelihood estimation, which is verified by the
numerical simulations and experiment study.
