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Extension of Autocovariance Coefficients Sequence for Periodically Correlated Processes

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  • Sophie Lambert‐Lacroix

Abstract

. 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.

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  • Sophie Lambert‐Lacroix, 2005. "Extension of Autocovariance Coefficients Sequence for Periodically Correlated Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 423-435, May.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:3:p:423-435
    DOI: 10.1111/j.1467-9892.2004.00409.x
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    References listed on IDEAS

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    1. D. Alpay & A. Chevreuil & Ph. Loubaton, 2001. "An Extension Problem For Discrete‐Time Periodically Correlated Stochastic Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(1), pages 1-11, January.
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    Cited by:

    1. Georgi N. Boshnakov & Sophie Lambert‐Lacroix, 2009. "Maximum entropy for periodically correlated processes from nonconsecutive autocovariance coefficients," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(5), pages 467-486, September.
    2. Boshnakov, Georgi N. & Lambert-Lacroix, Sophie, 2012. "A periodic Levinson-Durbin algorithm for entropy maximization," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 15-24, January.
    3. Mitra Ghanbarzadeh & Mina Aminghafari, 2016. "A Wavelet Characterization of Continuous-Time Periodically Correlated Processes with Application to Simulation," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(6), pages 741-762, November.

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