IN PARAMETRIC MODELLING OF TIME SERIES ,

Autoregressive-moving average (ARnA) models, and their autoregressive (AR) counterparts, are useful approximants to the kinds of random processes commonly encountered in discrete-time signal processing applications. Such models may be used to compress data in low bit-rate information transmission, improve frequency resolution In spectrum analysis, and to forecast in economic, meteorological, and other time series. In this paper we discuss several aspects of the maximum likelihood theory of parameter identification in ARMA and AR models. We highlight the initial condition problem encountered when identifying AMA or AR models from finite data records and propose several methods for computing exact and approximate likelihood. Several new interpretations are given for the innovation representation of an AIA process. Computationally efficient lattice and fast Kalman filters are proposed for the computation of exact likelihood.

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