The Wold decomposition of Hilbertian periodically correlated processes
Authors:
A. Zamani, Z. Sajjadnia and M. Hashemi
Journal:
Theor. Probability and Math. Statist. 101 (2020), 119-127
MSC (2020):
Primary 60G05, 62M10
DOI:
https://doi.org/10.1090/tpms/1116
Published electronically:
January 5, 2021
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Additional Information
Abstract: The Wold decomposition of stationary processes is widely applied in time series prediction and provides interesting insights into the structure of stationary stochastic processes. In 1971, Kallianpur and Mandrekar, using the notion of resolution of identity and unitary operators, presented the Wold decomposition for weakly stationary stochastic processes with values in infinite dimensional separable Hilbert spaces. This paper aims to expand the idea of Wold decomposition to Hilbertian periodically correlated processes, applying the concept of ${\mathcal {L}}$-closed subspaces.
References
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Additional Information
A. Zamani
Affiliation:
Department of Statistics, Faculty of Science, Shiraz University, Shiraz, Iran
Address at time of publication:
Department of Statistics, Faculty of Science, Shiraz University, Shiraz, Iran
Email:
zamania@shirazu.ac.ir
Z. Sajjadnia
Affiliation:
Department of Statistics, Faculty of Science, Shiraz University, Shiraz, Iran
Email:
sajjadnia@shirazu.ac.ir
M. Hashemi
Affiliation:
Department of Statistics,University of Khansar, Khansar, Iran
Email:
hashemi@khansar-cmc.ac.ir
Keywords:
$H$-valued random variables,
${\mathcal {L}}$-closed subspaces,
moving average representation,
periodically correlated processes,
Wold decomposition
Received by editor(s):
October 26, 2018
Published electronically:
January 5, 2021
Additional Notes:
This work was supported by University of Khansar under contract number khansar-cmc-102.
Article copyright:
© Copyright 2020
American Mathematical Society
