A new multivariate equation-error autoregressive moving average system with conditional heteroscedastic noise: Maximum likelihood identification

Abstract

The aim of this paper is to deal with the problem of conditional heteroscedastic noise in multivariate systems. In this regard, a new multivariate equation-error system with colored noise is introduced, in which the noise conditional variance varies with time and the noise exhibits a GARCH process. Thus, in this our new approach, both the time dependency and probability distribution of noise samples shall be identified. Based on the maximum likelihood principle and orthogonality of parameters, the problem of multivariate system identification is reduced into two separate maximum likelihood problems. An iterative algorithm is proposed, which can efficiently estimate the problem parameters based on gradient reduction and nonlinear optimization. Besides, a bootstrap algorithm is applied for assessing the accuracy of estimators. Also, some asymptotic result of proposed method in large sample size is provided. According to bootstrap simulation results, the proposed algorithm can effectively estimate the parameters of the system with conditional heteroscedastic noise and provides more accurate parameter estimates with a much lower confidence interval, compared to the least square method.