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Econometrics 2016, 4(3), 37; doi:10.3390/econometrics4030037

Generalized Fractional Processes with Long Memory and Time Dependent Volatility Revisited

1
School of Mathematics and Statistics, The University of Sydney, Sydney 2006, Australia
2
Faculty of Economics, Soka University, Tokyo 192-8577, Japan
*
Author to whom correspondence should be addressed.
Academic Editor: Kerry Patterson
Received: 15 January 2016 / Revised: 3 August 2016 / Accepted: 15 August 2016 / Published: 5 September 2016
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Abstract

In recent years, fractionally-differenced processes have received a great deal of attention due to their flexibility in financial applications with long-memory. This paper revisits the class of generalized fractionally-differenced processes generated by Gegenbauer polynomials and the ARMA structure (GARMA) with both the long-memory and time-dependent innovation variance. We establish the existence and uniqueness of second-order solutions. We also extend this family with innovations to follow GARCH and stochastic volatility (SV). Under certain regularity conditions, we give asymptotic results for the approximate maximum likelihood estimator for the GARMA-GARCH model. We discuss a Monte Carlo likelihood method for the GARMA-SV model and investigate finite sample properties via Monte Carlo experiments. Finally, we illustrate the usefulness of this approach using monthly inflation rates for France, Japan and the United States. View Full-Text
Keywords: GARMA; GARCH; stochastic volatility; long-memory; fractional differencing GARMA; GARCH; stochastic volatility; long-memory; fractional differencing
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Peiris, M.S.; Asai, M. Generalized Fractional Processes with Long Memory and Time Dependent Volatility Revisited. Econometrics 2016, 4, 37.

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