## Statistical Science

### Fractionally Differenced Gegenbauer Processes with Long Memory: A Review

#### Abstract

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.

#### Article information

Source
Statist. Sci., Volume 33, Number 3 (2018), 413-426.

Dates
First available in Project Euclid: 13 August 2018

https://projecteuclid.org/euclid.ss/1534147230

Digital Object Identifier
doi:10.1214/18-STS649

Mathematical Reviews number (MathSciNet)
MR3843383

Zentralblatt MATH identifier
06991127

#### Citation

Dissanayake, G. S.; Peiris, M. S.; Proietti, T. Fractionally Differenced Gegenbauer Processes with Long Memory: A Review. Statist. Sci. 33 (2018), no. 3, 413--426. doi:10.1214/18-STS649. https://projecteuclid.org/euclid.ss/1534147230

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