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Spectral measures of PARMA sequences
Author(s) -
Wyłomańska Agnieszka
Publication year - 2008
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/j.1467-9892.2007.00541.x
Subject(s) - mathematics , autoregressive model , autoregressive–moving average model , measure (data warehouse) , spectral analysis , bounded function , multivariate statistics , spectral measure , spectrum (functional analysis) , spectral properties , mathematical analysis , statistics , pure mathematics , data mining , computer science , physics , computational chemistry , chemistry , quantum mechanics , spectroscopy
. The aim of this article is to give a complete description of the spectral measure of periodic autoregressive moving‐average (PARMA) system in terms of its coefficients. In the analysis we use the spectral theory of strongly harmonizable sequences presented in Hurd [ Journal of Multivariate Analysis (1989) Vol. 29, pp. 53–67] and the form of the unique bounded solution of ARMA model with periodic coefficients. As an application of the theoretical results, we present some examples of the spectral measures for PARMA models.