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Modelling Long-Memory Volatilities With Leverage Effect: Almsv Versus Fiegarch

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  • Esther Ruiz
  • Helena Veiga

Abstract

In this paper, we propose a new stochastic volatility model, called A-LMSV, to cope simultaneously with the leverage effect and long-memory. We derive its statistical properties and compare them with the properties of the FIEGARCH model. We show that the dependence of the autocorrelations of squares on the parameters measuring the asymmetry and the persistence is different in both models. The kurtosis and autocorrelations of squares do not depend on the asymmetry in the A-LMSV model while they increase with the asymmetry in the FIEGARCH model. Furthermore, the autocorrelations of squares increase with the persistence in the A-LMSV model and decrease in the FIEGARCH model. On the other hand, the autocorrelations of absolute returns increase with the magnitude of the asymmetry in the FIEGARCH model while they can increase or decrease depending on the sign of the asymmetry in the L-MSV model. Finally, the cross-correlations between squares and original observations are, in general, larger in the FIEGARCH model than in the ALMSV model. The results are illustrated by fitting both models to represent the dynamic evolution of volatilities of daily returns of the S&P500 and DAX indexes.

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Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws066016.

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Date of creation: Oct 2006
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Handle: RePEc:cte:wsrepe:ws066016

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Cited by:
  1. Kwan, Wilson & Li, Wai Keung & Li, Guodong, 2012. "On the estimation and diagnostic checking of the ARFIMA–HYGARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3632-3644.
  2. Lopes, Sílvia R.C. & Prass, Taiane S., 2014. "Theoretical results on fractionally integrated exponential generalized autoregressive conditional heteroskedastic processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 278-307.
  3. Roengchai Tansuchat & Chia-Lin Chang & Michael McAleer, 2009. "Modelling Long Memory Volatility in Agricultural Commodity Futures Returns," CARF F-Series CARF-F-183, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  4. Shinichiro Shirota & Takayuki Hizu & Yasuhiro Omori, 2013. "Realized Stochastic Volatility with Leverage and Long Memory," CIRJE F-Series CIRJE-F-880, CIRJE, Faculty of Economics, University of Tokyo.
  5. Borovkova, Svetlana & Permana, Ferry J., 2009. "Implied volatility in oil markets," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2022-2039, April.
  6. Shirota, Shinichiro & Hizu, Takayuki & Omori, Yasuhiro, 2014. "Realized stochastic volatility with leverage and long memory," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 618-641.
  7. Helena Veiga, 2009. "Financial Stylized Facts and the Taylor-Effect in Stochastic Volatility Models," Economics Bulletin, AccessEcon, vol. 29(1), pages 265-276.
  8. Taiane S. Prass & S\'ilvia R. C. Lopes, 2013. "Risk Measure Estimation On Fiegarch Processes," Papers 1305.5238, arXiv.org.
  9. María José Rodríguez & Esther Ruiz, 2009. "GARCH models with leverage effect : differences and similarities," Statistics and Econometrics Working Papers ws090302, Universidad Carlos III, Departamento de Estadística y Econometría.
  10. Caporale, Guglielmo Maria & Gil-Alana, Luis A., 2008. "Modelling the US, UK and Japanese unemployment rates: Fractional integration and structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4998-5013, July.
  11. Xiuping Mao & Esther Ruiz & Helena Veiga, 2013. "One for all : nesting asymmetric stochastic volatility models," Statistics and Econometrics Working Papers ws131110, Universidad Carlos III, Departamento de Estadística y Econometría.
  12. Haas, Markus, 2009. "Persistence in volatility, conditional kurtosis, and the Taylor property in absolute value GARCH processes," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1674-1683, August.
  13. Montero, José M. & García-Centeno, Maria C. & Fernández-Avilés, Gema, 2011. "Modelling the Volatility of the Spanish Wholesale Electricity Spot Market. Asymmetric GARCH Models vs. Threshold ARSV model/Modelización de la volatilidad en el mercado eléctrico español. Modelos G," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 29, pages 597-616, Agosto.
  14. 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.
  15. Helena Veiga, 2006. "A Two Factor Long Memory Stochastic Volatility Model," Statistics and Econometrics Working Papers ws061303, Universidad Carlos III, Departamento de Estadística y Econometría.

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