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Large Sample Properties of Parameter Estimates for Periodic ARMA Models
Author(s) -
Basawa I. V.,
Lund Robert
Publication year - 2001
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 - 10.1111/1467-9892.00246
Subject(s) - mathematics , autoregressive model , invertible matrix , autoregressive–moving average model , moving average , univariate , series (stratigraphy) , moving average model , statistics , limit (mathematics) , estimation theory , autoregressive integrated moving average , covariance matrix , time series , multivariate statistics , mathematical analysis , paleontology , biology , pure mathematics
This paper studies the asymptotic properties of parameter estimates for causal and invertible periodic autoregressive moving‐average (PARMA) time series models. A general limit result for PARMA parameter estimates with a moving‐average component is derived. The paper presents examples that explicitly identify the limiting covariance matrix for parameter estimates from a general periodic autoregression (PAR), a first‐order periodic moving average (PMA(1)), and the mixed PARMA(1,1) model. Some comparisons and contrasts to univariate and vector autoregressive moving‐average sequences are made.