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State space modeling of Gegenbauer processes with long memory

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  • Dissanayake, G.S.
  • Peiris, M.S.
  • Proietti, T.

Abstract

An approximation of a Gegenbauer autoregressive moving average (GARMA) process with long memory using a finite order moving average (MA) representation is considered. The state space form of the MA approximation is developed and the corresponding estimates are obtained by pseudo maximum likelihood using the Kalman filter. For comparative purposes the same exercise is executed with an autoregressive (AR) approximation. Using an extensive Monte Carlo experiment, optimal order of the chosen MA approximation is established, and found it was not very large (around 35) and rather insensitive to the sample size. Further evidence suggests the approximation is reliable for forecasting and signal extraction with periodic long memory components. A rolling forecasting experiment was performed to validate the choice of optimal order of both AR and MA approximations in terms of predictive accuracy. Finally, the proposed methodology was applied to two yearly sunspots time series, and compared with corresponding results proposed in the literature.

Suggested Citation

  • Dissanayake, G.S. & Peiris, M.S. & Proietti, T., 2016. "State space modeling of Gegenbauer processes with long memory," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 115-130.
    • Handle: RePEc:eee:csdana:v:100:y:2016:i:c:p:115-130
    DOI: 10.1016/j.csda.2014.09.014
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    2. Kechagias, Stefanos & Pipiras, Vladas & Zoubouloglou, Pavlos, 2024. "Cyclical long memory: Decoupling, modulation, and modeling," Stochastic Processes and their Applications, Elsevier, vol. 175(C).
    3. Paul M. Beaumont & Aaron D. Smallwood, 2024. "Conditional sum of squares estimation of k-factor GARMA models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(3), pages 501-543, September.
    4. Phillip, Andrew & Chan, Jennifer & Peiris, Shelton, 2020. "On generalized bivariate student-t Gegenbauer long memory stochastic volatility models with leverage: Bayesian forecasting of cryptocurrencies with a focus on Bitcoin," Econometrics and Statistics, Elsevier, vol. 16(C), pages 69-90.
    5. Becker, Janis & Hollstein, Fabian & Prokopczuk, Marcel & Sibbertsen, Philipp, 2019. "The Memory of Beta Factors," Hannover Economic Papers (HEP) dp-661, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    6. Richard Hunt & Shelton Peiris & Neville Weber, 2022. "Estimation methods for stationary Gegenbauer processes," Statistical Papers, Springer, vol. 63(6), pages 1707-1741, December.
    7. Federico Maddanu & Tommaso Proietti, 2023. "Trends in atmospheric ethane," Climatic Change, Springer, vol. 176(5), pages 1-23, May.
    8. Jan Beran & Jeremy Näscher & Fabian Pietsch & Stephan Walterspacher, 2024. "Testing for periodicity at an unknown frequency under cyclic long memory, with applications to respiratory muscle training," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(4), pages 705-731, December.

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