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Recursive Prediction and Likelihood Evaluation for Periodic ARMA Models
Author(s) -
Lund Robert,
Basawa I. V.
Publication year - 2000
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00174
Subject(s) - autoregressive–moving average model , recursion (computer science) , autoregressive model , mathematics , multivariate statistics , moving average , series (stratigraphy) , autoregressive integrated moving average , moving average model , gaussian , time series , statistics , algorithm , paleontology , physics , quantum mechanics , biology
This paper explores recursive prediction and likelihood evaluation techniques for periodic autoregressive moving‐average (PARMA) time series models. The innovations algorithm is used to develop a simple recursive scheme for computing one‐step‐ahead predictors and their mean squared errors. The asymptotic form of this recursion is explored. The prediction results are then used to develop an efficient (and exact) PARMA likelihood evaluation algorithm for Gaussian series. We then show how a multivariate autoregressive moving average (ARMA) likelihood can be evaluated by writing the multivariate ARMA model in PARMA form. Explicit calculations for PARMA(1, 1) models and periodic autoregressions are included.