Functional Series Time-dependent AutoRegressive Moving Average (TARMA) models form an important class of nonstationary stochastic models offering high parsimony, tracking of “fast” and “slow” variations, high accuracy and resolution, as well as accurate capturing of both resonances and antiresonances. This paper considers the estimation of Functional Series TARMA models with polynomial functional spaces based upon a novel matrix algebra that is isomorphic to that of the noncommutative ring of time-varying polynomial operators expressed in terms of the model’s functional spaces. The Generalized estimation method introduced offers important advantages, such as the use of properly contracted functional spaces that is necessary for the elimination of asymptotic bias errors, the ability to handle AR and MA functional spaces of different dimensionalities, as well as improved accuracy through a streamlined realization. The method’s excellent performance characteristics are confirmed via Monte Carlo experiments and comparisons with an earlier Polynomial-Algebraic approach and the adaptive Recursive Maximum Likelihood ARMA method.
On the Estimation of Nonstationary Functional Series TARMA Models: An Isomorphic Matrix Algebra Based Method1
Contributed by the Dynamic Systems and Control Division for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the Dynamic Systems and Control Division January 30, 2001. Associate Editor: A. G. Ulsoy.
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Fouskitakis , G. N., and Fassois, S. D. (January 30, 2001). "On the Estimation of Nonstationary Functional Series TARMA Models: An Isomorphic Matrix Algebra Based Method." ASME. J. Dyn. Sys., Meas., Control. December 2001; 123(4): 601–610. https://doi.org/10.1115/1.1409551
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