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J. Risk Financial Manag. 2017, 10(4), 23; https://doi.org/10.3390/jrfm10040023

Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models

1
School of Mathematics and Statistics, University of Sydney, Camperdown, NSW 2006, Australia
2
Faculty of Economics, Soka University, Tokyo 192-8577, Japan
3
Department of Quantitative Finance, National Tsing Hua University, Hsinchu 300, Taiwan
4
Discipline of Business Analytics, University of Sydney Business School, Darlington, NSW 2006, Australia
5
Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam, 3062 PA Rotterdam, The Netherlands
6
Department of Quantitative Economics, Complutense University of Madrid, 28040 Madrid, Spain
7
Institute of Advanced Studies, Yokohama National University, Yokohama, Kanagawa 240-8501, Japan
*
Author to whom correspondence should be addressed.
Received: 30 October 2017 / Revised: 4 December 2017 / Accepted: 8 December 2017 / Published: 12 December 2017
(This article belongs to the Special Issue Risk Analysis and Portfolio Modelling)
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Abstract

This paper considers a flexible class of time series models generated by Gegenbauer polynomials incorporating the long memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the corresponding statistical properties of this model, discuss the spectral likelihood estimation and investigate the finite sample properties via Monte Carlo experiments. We provide empirical evidence by applying the GLMSV model to three exchange rate return series and conjecture that the results of out-of-sample forecasts adequately confirm the use of GLMSV model in certain financial applications. View Full-Text
Keywords: stochastic volatility; GARCH models; Gegenbauer polynomial; long memory; spectral likelihood; estimation; forecasting stochastic volatility; GARCH models; Gegenbauer polynomial; long memory; spectral likelihood; estimation; forecasting
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, S.; Asai, M.; McAleer, M. Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models. J. Risk Financial Manag. 2017, 10, 23.

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