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Convolution Process Revisited in Finite Location Mixtures and GARFISMA Long Memory Time Series

In: Flexible Nonparametric Curve Estimation

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  • G. S. Dissanayake

    (University of Sydney, NSW Ministry of Health and School of Mathematics and Statistics)

Abstract

This article focuses on the utilisation of the convolution process by specialist theoretical statisticians representing two distinct analytical domains of the subject classified as nonparametric statistics and time series analysis. Main contribution is established through a discussion centered around some comparative properties of the convolution process, where the relevant operator performs similar yet different operations on differing statistical operands. As specific cases, examples from the considered subject areas in theoretical statistics known as finite location mixture distributions and fractionally integrated Gegenbauer autoregressive moving average (GARMA) seasonal long memory time series are presented to illustrate the overall value of convolution in arriving at closed form solutions. Importance and robustness of the process are revelations highlighted in the article as a secondary contribution.

Suggested Citation

  • G. S. Dissanayake, 2024. "Convolution Process Revisited in Finite Location Mixtures and GARFISMA Long Memory Time Series," Springer Books, in: Hassan Doosti (ed.), Flexible Nonparametric Curve Estimation, pages 81-93, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-66501-1_4
    DOI: 10.1007/978-3-031-66501-1_4
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