Calculation of the Fisher Information Matrix for Periodic ARMA Models

The present article is mainly concerned with the calculation of the Fisher information matrix associated to a periodic autoregressive moving average model (P-ARMA). We provide a computation algorithm based on the conditional likelihood function expression. The established algorithm extends Klein and...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2005-04, Vol.34 (4), p.891-903
Main Authors: BENTARZI, MOHAMED, AKNOUCHE, ABDELHAKIM
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fisher information matrix
Inference from stochastic processes
time series analysis
Mathematics
Parametric inference
Periodic autocovariance function
Periodically correlated autoregressive moving average process
Primary 62M10
Probability and statistics
Recursive estimation
Sciences and techniques of general use
Secondary 62F15
Statistics
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Summary:The present article is mainly concerned with the calculation of the Fisher information matrix associated to a periodic autoregressive moving average model (P-ARMA). We provide a computation algorithm based on the conditional likelihood function expression. The established algorithm extends Klein and Mélard's algorithm ( 1989 ) elaborated for the classical ARMA models, to the case of periodic autoregressive moving average models. Moreover, for the application of this algorithm, we provide a procedure to compute the theoretical periodic autocovariance function in terms of the parameters of the periodic model. In addition, we give a necessary and sufficient condition for non singular Fisher information matrix of a periodic ARMA model.
ISSN:0361-0926
1532-415X
DOI:10.1081/STA-200054428