The Efficient Estimation of Stationary Multiple Time Series Mixed Models: Theory and Algorithms.
STATE UNIV OF NEW YORK AT BUFFALO AMHERST STATISTICAL SCIENCE DIV
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The d-dimensional vector mixed autoregressive moving average time series model plays an important role in the statistical analysis of a wide variety of scientific data, including work in the physical, social, economic, and medical sciences. The statistical theory of the mixed model has been developed in some detail for d 1. The corresponding theory for multidimensional mixed time series is presently being developed by various authors, with many problems left to be solved. The aim of this thesis is to contribute to this developing theory. It provides a systematic presentation of the algebraic relationships between various parametrizations of the mixed scheme, and extends some of the results for d 1 to the case d 1. Further consideration is the theory of estimation of the parameters of pure autoregressive and moving average processes, as well as the mixed process. Of particular interest are 1 the derivation of the information matrices of the parameters of a mixed process, 2 an extension of the Parzen-Clevenson method of estimating the autocovariances of a scalar moving average process to the multiple case, and 3 two algorithms for determining if a multiple autoregressive process is stationary.
- Statistics and Probability