Model Identification and Estimation of NonGaussian ARMA Processes.

摘要

Finite parameter models of ARMA type have been used extensively in many applications. Under the usual Gaussian assumption, the second order analysis will not be able to discriminate among competing models which give the same correlation structure. In many applications the innovation process is non-Gaussian. In this case, analysis using higher order moments will identify the model uniquely without the usual invertibility assumption. This in turn will affect the forecasting based on the non-Gaussian model. We present a method which uses bispectral analysis and the Pade approximation. We show that the method will consistently identify the order of the ARMA model and estimate the parameters of the model. One could also deconvolve the process to estimate the innovative process which will provide information for possible more efficient maximum likelihood estimation of the parameters. Asymptotic distributions are given, and a few examples are presented to illustrate the effectiveness of the method. (Author)