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August 2018 Fractionally Differenced Gegenbauer Processes with Long Memory: A Review
G. S. Dissanayake, M. S. Peiris, T. Proietti
Statist. Sci. 33(3): 413-426 (August 2018). DOI: 10.1214/18-STS649


The main objective of this paper is to review and promote the usefulness of generalized fractionally differenced Gegenbauer processes in time series and econometric research endeavours. In particular, theoretical and computational aspects centered around fractionally differenced Gegenbauer processes with long memory together with a number of interesting and elegant extensions will be discussed. In-depth conceptual developments and large scale simulation study results are presented for clarity and completeness. This survey highlights a number of gaps in the existing literature of this subject area and becomes a valuable reference source for time series practitioners.


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G. S. Dissanayake. M. S. Peiris. T. Proietti. "Fractionally Differenced Gegenbauer Processes with Long Memory: A Review." Statist. Sci. 33 (3) 413 - 426, August 2018.


Published: August 2018
First available in Project Euclid: 13 August 2018

zbMATH: 06991127
MathSciNet: MR3843383
Digital Object Identifier: 10.1214/18-STS649

Keywords: fractional difference , Gegenbauer process , heteroskedasticity , invertibility , long memory , Spectral density , stationarity , Volatility

Rights: Copyright © 2018 Institute of Mathematical Statistics


Vol.33 • No. 3 • August 2018
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