On the parameter estimation of ARMA(p,q) model by approximate Bayesian computation

TL;DR

This paper introduces an approximate Bayesian computation method for estimating ARMA(p,q) model parameters, transforming the problem into simpler models and using autocorrelation-based statistics for improved accuracy and efficiency.

Contribution

It proposes a novel ABC-based approach that enhances parameter estimation accuracy for ARMA models by selecting informative low-dimensional statistics.

Findings

The method outperforms maximum likelihood estimation in accuracy.

Numerical simulations confirm the effectiveness of the approach.

Transforming ARMA into MA models simplifies estimation.

Abstract

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.