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Extension of Autocovariance Coefficients Sequence for Periodically Correlated Processes
Author(s) -
LambertLacroix Sophie
Publication year - 2005
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.1467-9892.2004.00409.x
Subject(s) - autocovariance , mathematics , autocorrelation , partial autocorrelation function , autoregressive model , autocorrelation matrix , stationary process , extension (predicate logic) , sequence (biology) , mathematical analysis , statistical physics , statistics , time series , fourier transform , computer science , autoregressive integrated moving average , physics , biology , genetics , programming language
. The extension of stationary process autocorrelation coefficient sequence is a classical problem in the field of spectral estimation. In this note, we treat this extension problem for the periodically correlated processes by using the partial autocorrelation function. We show that the theory of the non‐stationary processes can be adapted to the periodically correlated processes. The partial autocorrelation function has a clear advantage for parameterization over the autocovariance function which should be checked for non‐negative definiteness. In this way, we show that contrary to the stationary case, the Yule–Walker equations (for a periodically correlated process) is no longer a tool for extending the first autocovariance coefficients to an autocovariance function. Next, we treat the extension problem and present a maximum entropy method extension through the the partial autocorrelation function. We show that the solution maximizing the entropy is a periodic autoregressive process and compare this approach with others.