Time series model identification using vector sample correlation function

Abstract

The primary purpose of this thesis is to develop a new theory and technique for determining the order of a general autoregressive moving average (ARMA) model which can represent a stationary or a homogeneously nonstationary process. Based on the consistent autoregressive estimates produced by iterated regressions, two kinds of statistical tools are proposed; one is the vector sample autocorrelation function (VSACF) for univariate model and the other is vector sample cross correlation function (VSCCF) for multivariate model. Using these tools, model identification techniques are developed which have the special feature that the model order can be selected automatically without human intervention. A variety of approaches for time series model identification are surveyed and categorized as the before estimation, after-estimation and mixed methods. Among the various methods, the mixed method appears to be one of the most powerful tool which, however, can not be automatically performed. Secondly, the new statistical tool, named VSACF, is defined and the theorems are given to show the asymptotic behavior of the VSACF for the general ARMA(p,q) model. By the property of the VSACF array, model identification procedure needs only checking whether the North-West elements are zeroes, which make the procedure simple and automatic. The adequate value of the vector size is suggested with the analysis several generated and actual data. Finally, for multivariate model identification, the VSCCF is defined by direct generalization of the VASCF. The pattern of the VSCCF for the vector ARMA model is proved to be similar to that of the VSACF for general ARMA model. The results of the illustrative examples suggest that the VSCCF approach can be completely automated for the identification of univariate and multivariate time series.