Realized stochastic volatility models with generalized Gegenbauer long memory

Manabu Asai; Michael McAleer; Shelton Peiris

doi:10.1016/j.ecosta.2018.12.005

Realized stochastic volatility models with generalized Gegenbauer long memory

Manabu Asai^*, Michael McAleer, Shelton Peiris

^*Corresponding author for this work

Econometrics

Research output: Contribution to journal › Article › Academic › peer-review

6 Citations (Scopus)

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Abstract

Fractionally differenced processes have received a great deal of attention due to their flexibility in financial applications with long memory. In this paper, new realized stochastic volatility (RSV) models are developed: one is a RSV model with general Gegenbauer long memory (GGLM), while the other is a 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, a two step method is suggested: the location parameters for the peaks of the power spectrum are estimated in the first step, while the remaining parameters are estimated based on the Whittle likelihood in the second step. Monte Carlo experiments give results for investigating the finite sample properties of the estimators, with a quasi-likelihood ratio test of the RSV–SLM model against the RSV–GGLM model. The RSV–GGLM and RSV–SLM models are applied to three stock market indices, for which the estimation and forecasting results indicate the adequacy of considering general long memory.

Original language	English
Pages (from-to)	42-54
Number of pages	13
Journal	Econometrics and Statistics
Volume	16
DOIs	https://doi.org/10.1016/j.ecosta.2018.12.005
Publication status	Published - Oct 2020

Bibliographical note

Funding Information:
The authors are most grateful to Yoshi Baba, Erricos Kontoghiorghes, the associate editor, and two anonymous reviewers for very helpful comments and suggestions. The first author acknowledges the financial support of the Japan Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science ( JSPS KAKENHI JP16K03603 ), and the Australian Academy of Science. The second author is most grateful for the financial support of the Australian Research Council, National Science Council, Ministry of Science and Technology (MOST), Taiwan, and the Japan Society for the Promotion of Science. The third author acknowledges the support from the Faculty of Economics at Soka University

Funding Information:
The authors are most grateful to Yoshi Baba, Erricos Kontoghiorghes, the associate editor, and two anonymous reviewers for very helpful comments and suggestions. The first author acknowledges the financial support of the Japan Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science (JSPS KAKENHI JP16K03603), and the Australian Academy of Science. The second author is most grateful for the financial support of the Australian Research Council, National Science Council, Ministry of Science and Technology (MOST), Taiwan, and the Japan Society for the Promotion of Science. The third author acknowledges the support from the Faculty of Economics at Soka University

Publisher Copyright:
© 2019 EcoSta Econometrics and Statistics

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10.1016/j.ecosta.2018.12.005

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title = "Realized stochastic volatility models with generalized Gegenbauer long memory",

abstract = "Fractionally differenced processes have received a great deal of attention due to their flexibility in financial applications with long memory. In this paper, new realized stochastic volatility (RSV) models are developed: one is a RSV model with general Gegenbauer long memory (GGLM), while the other is a 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, a two step method is suggested: the location parameters for the peaks of the power spectrum are estimated in the first step, while the remaining parameters are estimated based on the Whittle likelihood in the second step. Monte Carlo experiments give results for investigating the finite sample properties of the estimators, with a quasi-likelihood ratio test of the RSV–SLM model against the RSV–GGLM model. The RSV–GGLM and RSV–SLM models are applied to three stock market indices, for which the estimation and forecasting results indicate the adequacy of considering general long memory.",

author = "Manabu Asai and Michael McAleer and Shelton Peiris",

note = "Funding Information: The authors are most grateful to Yoshi Baba, Erricos Kontoghiorghes, the associate editor, and two anonymous reviewers for very helpful comments and suggestions. The first author acknowledges the financial support of the Japan Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science ( JSPS KAKENHI JP16K03603 ), and the Australian Academy of Science. The second author is most grateful for the financial support of the Australian Research Council, National Science Council, Ministry of Science and Technology (MOST), Taiwan, and the Japan Society for the Promotion of Science. The third author acknowledges the support from the Faculty of Economics at Soka University Funding Information: The authors are most grateful to Yoshi Baba, Erricos Kontoghiorghes, the associate editor, and two anonymous reviewers for very helpful comments and suggestions. The first author acknowledges the financial support of the Japan Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science (JSPS KAKENHI JP16K03603), and the Australian Academy of Science. The second author is most grateful for the financial support of the Australian Research Council, National Science Council, Ministry of Science and Technology (MOST), Taiwan, and the Japan Society for the Promotion of Science. The third author acknowledges the support from the Faculty of Economics at Soka University Publisher Copyright: {\textcopyright} 2019 EcoSta Econometrics and Statistics",

year = "2020",

month = oct,

doi = "10.1016/j.ecosta.2018.12.005",

language = "English",

volume = "16",

pages = "42--54",

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AU - McAleer, Michael

AU - Peiris, Shelton

N1 - Funding Information: The authors are most grateful to Yoshi Baba, Erricos Kontoghiorghes, the associate editor, and two anonymous reviewers for very helpful comments and suggestions. The first author acknowledges the financial support of the Japan Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science ( JSPS KAKENHI JP16K03603 ), and the Australian Academy of Science. The second author is most grateful for the financial support of the Australian Research Council, National Science Council, Ministry of Science and Technology (MOST), Taiwan, and the Japan Society for the Promotion of Science. The third author acknowledges the support from the Faculty of Economics at Soka University Funding Information: The authors are most grateful to Yoshi Baba, Erricos Kontoghiorghes, the associate editor, and two anonymous reviewers for very helpful comments and suggestions. The first author acknowledges the financial support of the Japan Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science (JSPS KAKENHI JP16K03603), and the Australian Academy of Science. The second author is most grateful for the financial support of the Australian Research Council, National Science Council, Ministry of Science and Technology (MOST), Taiwan, and the Japan Society for the Promotion of Science. The third author acknowledges the support from the Faculty of Economics at Soka University Publisher Copyright: © 2019 EcoSta Econometrics and Statistics

PY - 2020/10

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N2 - Fractionally differenced processes have received a great deal of attention due to their flexibility in financial applications with long memory. In this paper, new realized stochastic volatility (RSV) models are developed: one is a RSV model with general Gegenbauer long memory (GGLM), while the other is a 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, a two step method is suggested: the location parameters for the peaks of the power spectrum are estimated in the first step, while the remaining parameters are estimated based on the Whittle likelihood in the second step. Monte Carlo experiments give results for investigating the finite sample properties of the estimators, with a quasi-likelihood ratio test of the RSV–SLM model against the RSV–GGLM model. The RSV–GGLM and RSV–SLM models are applied to three stock market indices, for which the estimation and forecasting results indicate the adequacy of considering general long memory.

AB - Fractionally differenced processes have received a great deal of attention due to their flexibility in financial applications with long memory. In this paper, new realized stochastic volatility (RSV) models are developed: one is a RSV model with general Gegenbauer long memory (GGLM), while the other is a 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, a two step method is suggested: the location parameters for the peaks of the power spectrum are estimated in the first step, while the remaining parameters are estimated based on the Whittle likelihood in the second step. Monte Carlo experiments give results for investigating the finite sample properties of the estimators, with a quasi-likelihood ratio test of the RSV–SLM model against the RSV–GGLM model. The RSV–GGLM and RSV–SLM models are applied to three stock market indices, for which the estimation and forecasting results indicate the adequacy of considering general long memory.

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DO - 10.1016/j.ecosta.2018.12.005

M3 - Article

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SN - 2452-3062

VL - 16

SP - 42

EP - 54

JO - Econometrics and Statistics

JF - Econometrics and Statistics

ER -

Realized stochastic volatility models with generalized Gegenbauer long memory

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