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Moments and dynamic structure of a time-varying parameter stochastic volatility in mean model

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  • Antonis Demos

Abstract

This paper introduces and discusses some of the statistical properties of a time-varying parameter stochastic volatility (SV) in mean model. We derive the autocovariance function of an observed series, under the assumption that the conditional variance follows a flexible parameterization, which nests the autoregressive SV and the exponential GARCH specifications. Furthermore, the mean parameter can be time varying. We also present the autocovariance functions of higher orders and discuss identification issues. Our result can be applied so that the properties of the observed data may be compared with the theoretical properties of the models, thus facilitating model identification. Furthermore, they can be employed in the estimation and derivation of misspecification tests. Copyright Royal Economic Society, 2002

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  • Antonis Demos, 2002. "Moments and dynamic structure of a time-varying parameter stochastic volatility in mean model," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 345-357, June.
    • Handle: RePEc:ect:emjrnl:v:5:y:2002:i:2:p:345-357
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    Cited by:

    1. Giraitis, Liudas & Leipus, Remigijus & Robinson, Peter M. & Surgailis, Donatas, 2004. "LARCH, leverage, and long memory," LSE Research Online Documents on Economics 294, London School of Economics and Political Science, LSE Library.
    2. Sofia Anyfantaki & Antonis Demos, 2016. "Estimation and Properties of a Time-Varying EGARCH(1,1) in Mean Model," Econometric Reviews, Taylor & Francis Journals, vol. 35(2), pages 293-310, February.
    3. Liudas Giraitis, 2004. "LARCH, Leverage, and Long Memory," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 177-210.
    4. Demos Antonis & Kyriakopoulou Dimitra, 2019. "Finite-Sample Theory and Bias Correction of Maximum Likelihood Estimators in the EGARCH Model," Journal of Time Series Econometrics, De Gruyter, vol. 11(1), pages 1-20, January.
    5. Mao, Xiuping & Ruiz Ortega, Esther & Lopes Moreira Da Veiga, María Helena, 2013. "One for all : nesting asymmetric stochastic volatility models," DES - Working Papers. Statistics and Econometrics. WS ws131110, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. P. de Zea Bermudez & J. Miguel Marín & Helena Veiga, 2020. "Data cloning estimation for asymmetric stochastic volatility models," Econometric Reviews, Taylor & Francis Journals, vol. 39(10), pages 1057-1074, November.
    7. Walter Krämer & Philip Mess, 2012. "Structural Change and Spurious Persistence in Stochastic Volatility," Ruhr Economic Papers 0310, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    8. Rodríguez, Mª José & Ruiz Ortega, Esther, 2009. "GARCH models with leverage effect : differences and similarities," DES - Working Papers. Statistics and Econometrics. WS ws090302, Universidad Carlos III de Madrid. Departamento de Estadística.
    9. M. Karanasos & J. Kim, 2003. "Moments of the ARMA--EGARCH model," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 146-166, June.
    10. Mao, Xiuping & Czellar, Veronika & Ruiz, Esther & Veiga, Helena, 2020. "Asymmetric stochastic volatility models: Properties and particle filter-based simulated maximum likelihood estimation," Econometrics and Statistics, Elsevier, vol. 13(C), pages 84-105.
    11. Karanasos, Menelaos & Kim, Jinki, 2006. "A re-examination of the asymmetric power ARCH model," Journal of Empirical Finance, Elsevier, vol. 13(1), pages 113-128, January.
    12. Wilfredo Palma & Mauricio Zevallos, 2004. "Analysis of the correlation structure of square time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 529-550, July.
    13. Carnero, M. Angeles & Pérez, Ana, 2019. "Leverage effect in energy futures revisited," Energy Economics, Elsevier, vol. 82(C), pages 237-252.
    14. Antonis Demos, 2023. "Estimation of Asymmetric Stochastic Volatility in Mean Models," DEOS Working Papers 2309, Athens University of Economics and Business.
    15. Till Strohsal, 2013. "Testing the Preferred-Habitat Theory: The Role ofTime-Varying Risk Aversion," SFB 649 Discussion Papers SFB649DP2013-043, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. Krämer, Walter & Messow, Philip, 2012. "Structural Change and Spurious Persistence in Stochastic Volatility," Ruhr Economic Papers 310, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    17. Carol Alexander & Emese Lazar & Silvia Stanescu, 2010. "Analytic Moments for GARCH Processes," ICMA Centre Discussion Papers in Finance icma-dp2011-07, Henley Business School, University of Reading, revised Apr 2011.
    18. Antonis Demos, 2023. "Statistical Properties of Two Asymmetric Stochastic Volatility in Mean Models," DEOS Working Papers 2303, Athens University of Economics and Business.
    19. Alexander, Carol & Lazar, Emese & Stanescu, Silvia, 2021. "Analytic moments for GJR-GARCH (1, 1) processes," International Journal of Forecasting, Elsevier, vol. 37(1), pages 105-124.
    20. Giraitis, Liudas & Leipus, Remigijus & Robinson, Peter M. & Surgailis, Donatas, 2003. "LARCH, leverage and long memory," LSE Research Online Documents on Economics 2020, London School of Economics and Political Science, LSE Library.
    21. Pérez, Ana & Ruiz, Esther & Veiga, Helena, 2009. "A note on the properties of power-transformed returns in long-memory stochastic volatility models with leverage effect," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3593-3600, August.
    22. Mao, Xiuping & Ruiz, Esther & Veiga, Helena, 2017. "Threshold stochastic volatility: Properties and forecasting," International Journal of Forecasting, Elsevier, vol. 33(4), pages 1105-1123.
    23. María José Rodríguez & Esther Ruiz, 2012. "Revisiting Several Popular GARCH Models with Leverage Effect: Differences and Similarities," Journal of Financial Econometrics, Oxford University Press, vol. 10(4), pages 637-668, September.
    24. Liudas Giraitis & Remigijus Leipus & Peter M Robinson & Donatas Surgailis, 2003. "LARCH, Leverage and Long Memory," STICERD - Econometrics Paper Series 460, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    25. repec:zbw:rwirep:0310 is not listed on IDEAS

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