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Periodic Long-Memory GARCH Models

Author

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  • Silvano Bordignon
  • Massimiliano Caporin
  • Francesco Lisi

Abstract

A distinguishing feature of the intraday time-varying volatility of financial time series is given by the presence of long-range dependence of periodic type, due mainly to time-of-the-day phenomena. In this work, we introduce a model able to describe the empirical evidence given by this periodic long-memory behaviour. The model, named PLM-GARCH (Periodic Long-Memory GARCH), represents a natural extension of the FIGARCH model proposed for modelling long-range persistence of volatility. Periodic long memory versions of EGARCH (PLM-EGARCH) and of Log-GARCH (PLM-LGARCH) models are also examined. Some properties and characteristics of the models are given and finite sample performance of quasi-maximum likelihood estimation are studied with Monte Carlo simulations. Further possible extensions of the model to take into account multiple sources of periodic long-memory behaviour are proposed. Two empirical applications on intra-day financial time series are also provided.

Suggested Citation

  • Silvano Bordignon & Massimiliano Caporin & Francesco Lisi, 2009. "Periodic Long-Memory GARCH Models," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 60-82.
    • Handle: RePEc:taf:emetrv:v:28:y:2009:i:1-3:p:60-82
    DOI: 10.1080/07474930802387860
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    Cited by:

    1. Eduardo Rossi & Dean Fantazzini, 2015. "Long Memory and Periodicity in Intraday Volatility," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 13(4), pages 922-961.
    2. Caporin, Massimiliano & Preś, Juliusz & Torro, Hipolit, 2012. "Model based Monte Carlo pricing of energy and temperature Quanto options," Energy Economics, Elsevier, vol. 34(5), pages 1700-1712.
    3. Arteche, Josu & García-Enríquez, Javier, 2017. "Singular Spectrum Analysis for signal extraction in Stochastic Volatility models," Econometrics and Statistics, Elsevier, vol. 1(C), pages 85-98.
    4. Massimiliano Caporin & Angelo Ranaldo & Gabriel G. Velo, 2015. "Precious metals under the microscope: a high-frequency analysis," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 743-759, May.
    5. Leschinski, Christian & Sibbertsen, Philipp, 2014. "Model Order Selection in Seasonal/Cyclical Long Memory Models," Hannover Economic Papers (HEP) dp-535, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    6. Asai, Manabu & McAleer, Michael & Peiris, Shelton, 2020. "Realized stochastic volatility models with generalized Gegenbauer long memory," Econometrics and Statistics, Elsevier, vol. 16(C), pages 42-54.
    7. Massimiliano Caporin & Francesco Lisi, 2010. "Misspecification tests for periodic long memory GARCH models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(1), pages 47-62, March.
    8. Caporin, Massimiliano & Chang, Chia-Lin & McAleer, Michael, 2019. "Are the S&P 500 index and crude oil, natural gas and ethanol futures related for intra-day data?," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 50-70.
    9. Bordignon, Silvano & Caporin, Massimiliano & Lisi, Francesco, 2007. "Generalised long-memory GARCH models for intra-daily volatility," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5900-5912, August.
    10. Heni Boubaker & Bassem Saidane & Mouna Ben Saad Zorgati, 2022. "Modelling the dynamics of stock market in the gulf cooperation council countries: evidence on persistence to shocks," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-22, December.
    11. Khalifa, Ahmed & Caporin, Massimiliano & Hammoudeh, Shawkat, 2015. "Spillovers between energy and FX markets: The importance of asymmetry, uncertainty and business cycle," Energy Policy, Elsevier, vol. 87(C), pages 72-82.
    12. Voges, Michelle & Leschinski, Christian & Sibbertsen, Philipp, 2017. "Seasonal long memory in intraday volatility and trading volume of Dow Jones stocks," Hannover Economic Papers (HEP) dp-599, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    13. Caporin, Massimiliano & Ranaldo, Angelo & Velo, Gabriel G., 2013. "Stylized Facts and Dynamic Modeling of High-frequency Data on Precious Metals," Working Papers on Finance 1318, University of St. Gallen, School of Finance.
    14. Leschinski, Christian & Sibbertsen, Philipp, 2019. "Model order selection in periodic long memory models," Econometrics and Statistics, Elsevier, vol. 9(C), pages 78-94.
    15. Rajesh Mohnot, 2011. "Forecasting Forex Volatility In Turbulent Times," Global Journal of Business Research, The Institute for Business and Finance Research, vol. 5(1), pages 27-38.

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