Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory

Tinbergen Institute Discussion Paper 2017-105/III

27 Pages Posted: 6 Nov 2017

See all articles by Manabu Asai

Manabu Asai

Soka University - Faculty of Economics

Michael McAleer

Erasmus University Rotterdam - Erasmus School of Economics, Econometric Institute; Tinbergen Institute; University of Tokyo - Centre for International Research on the Japanese Economy (CIRJE), Faculty of Economics

Shelton Peiris

The University of Sydney

Date Written: November 1, 2017

Abstract

In recent years fractionally differenced processes have received a great deal of attention due to their flexibility in financial applications with long memory. In this paper, we develop a new realized stochastic volatility (RSV) model with general Gegenbauer long memory (GGLM), which encompasses a new RSV model with seasonal long memory (SLM). The RSV model uses the information from returns and realized volatility measures simultaneously. The long memory structure of both models can describe unbounded peaks apart from the origin in the power spectrum. For estimating the RSV-GGLM model, we suggest estimating the location parameters for the peaks of the power spectrum in the first step, and the remaining parameters based on the Whittle likelihood in the second step. We conduct Monte Carlo experiments for investigating the finite sample properties of the estimators, with a quasi-likelihood ratio test of RSV-SLM model against the RSV-GGLM model. We apply the RSV-GGLM and RSV-SLM model to three stock market indices. The estimation and forecasting results indicate the adequacy of considering general long memory.

Keywords: Stochastic Volatility, Realized Volatility Measure, Long Memory, Gegenbauer Polynomial, Seasonality, Whittle Likelihood

JEL Classification: C18, C21, C58

Suggested Citation

Asai, Manabu and McAleer, Michael and Peiris, Shelton, Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory (November 1, 2017). Tinbergen Institute Discussion Paper 2017-105/III, Available at SSRN: https://ssrn.com/abstract=3064736 or http://dx.doi.org/10.2139/ssrn.3064736

Manabu Asai (Contact Author)

Soka University - Faculty of Economics ( email )

1-236 Tangi-cho
Hachioji (city)
Tokyo, 192-8577
Japan

HOME PAGE: http://www.soka.ac.jp/en/#a01

Michael McAleer

Erasmus University Rotterdam - Erasmus School of Economics, Econometric Institute ( email )

Rotterdam
Netherlands

Tinbergen Institute

Rotterdam
Netherlands

University of Tokyo - Centre for International Research on the Japanese Economy (CIRJE), Faculty of Economics

Tokyo
Japan

Shelton Peiris

The University of Sydney ( email )

Sydney, New South Wales 2006
Australia
61293515764 (Phone)
61293514534 (Fax)

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