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Finite sample properties of a QML estimator of stochastic volatility models with long memory

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  • Pérez, Ana
  • Ruiz Ortega, Esther

Abstract

In this paper, we analyse the finite sample properties of a Quasi-Maximum Likelihood (QML) estimator of Long Memory Stochastic Volatility models based on the Whittle approximation of the Gaussian likelihood in the frequency domain. We extend previous studies by including in our Monte Carlo design all the parameters in the model and some more realistic cases. We show that for the parameter values usually encountered in practice, the properties of this estimator are such that inference is not reliable unless the sample size is extremely large. We also discuss a problem of nonidentification in the AutoRegressive Long Memory Stochastic Volatility Model when the volatility has a unit root and we show up its effect on the small sample properties of the QML estimators. The paper finishes with the empirical analysis of daily observations of the IBEX35 index of the Madrid Stock Exchange as an illustration of the problems faced when using this estimator with real time series.

Suggested Citation

  • Pérez, Ana & Ruiz Ortega, Esther, 1999. "Finite sample properties of a QML estimator of stochastic volatility models with long memory," DES - Working Papers. Statistics and Econometrics. WS 6360, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:6360
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    Cited by:

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    2. Asai Manabu & So Mike K.P., 2015. "Long Memory and Asymmetry for Matrix-Exponential Dynamic Correlation Processes," Journal of Time Series Econometrics, De Gruyter, vol. 7(1), pages 1-26, January.
    3. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    4. Ferraz, Rosemeire O. & Hotta, Luiz K., 2007. "Quasi-Maximum Likelihood Estimation of Long-Memory Stochastic Volatility Models," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 27(2), November.
    5. Adam McCloskey, 2012. "Estimation of the Long-Memory Stochastic Volatility Model Parameters that is Robust to Level Shifts and Deterministic Trends," Working Papers 2012-17, Brown University, Department of Economics.
    6. Arteche, Josu, 2004. "Gaussian semiparametric estimation in long memory in stochastic volatility and signal plus noise models," Journal of Econometrics, Elsevier, vol. 119(1), pages 131-154, March.
    7. Asai, Manabu & McAleer, Michael, 2015. "Forecasting co-volatilities via factor models with asymmetry and long memory in realized covariance," Journal of Econometrics, Elsevier, vol. 189(2), pages 251-262.
    8. Manabu Asai & Chia-Lin Chang & Michael McAleer, 2016. "Realized Matrix-Exponential Stochastic Volatility with Asymmetry, Long Memory and Spillovers," Documentos de Trabajo del ICAE 2016-15, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    9. Ruiz, Esther & Veiga, Helena, 2008. "Modelling long-memory volatilities with leverage effect: A-LMSV versus FIEGARCH," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2846-2862, February.
    10. Arteche, J., 2006. "Semiparametric estimation in perturbed long memory series," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2118-2141, December.
    11. Bhattacharya, Sharad Nath & Bhattacharya, Mousumi, 2013. "Long memory in return structures from developed markets," Cuadernos de Gestión, Universidad del País Vasco - Instituto de Economía Aplicada a la Empresa (IEAE).
    12. Grané, A. & Veiga, H., 2008. "Accurate minimum capital risk requirements: A comparison of several approaches," Journal of Banking & Finance, Elsevier, vol. 32(11), pages 2482-2492, November.
    13. 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.
    14. Adam McCloskey, 2013. "Estimation of the long-memory stochastic volatility model parameters that is robust to level shifts and deterministic trends," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 285-301, May.
    15. Ruiz Esther & Pérez Ana, 2012. "Maximally Autocorrelated Power Transformations: A Closer Look at the Properties of Stochastic Volatility Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(3), pages 1-33, September.
    16. Ana Pérez & Esther Ruiz, 2002. "Modelos de memoria larga para series económicas y financieras," Investigaciones Economicas, Fundación SEPI, vol. 26(3), pages 395-445, September.
    17. Trino-Manuel Ñíguez, 2003. "Volatility And Var Forecasting For The Ibex-35 Stock-Return Index Using Figarch-Type Processes And Different Evaluation Criteria," Working Papers. Serie AD 2003-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    18. Asai, Manabu & Chang, Chia-Lin & McAleer, Michael, 2022. "Realized matrix-exponential stochastic volatility with asymmetry, long memory and higher-moment spillovers," Journal of Econometrics, Elsevier, vol. 227(1), pages 285-304.

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