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A Mixture Multiplicative Error Model for Realized Volatility

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  • Markku Lanne

Abstract

A multiplicative error model with time-varying parameters and an error term following a mixture of gamma distributions is introduced. The model is fitted to the daily realized volatility series of deutschemark/dollar and yen/dollar returns and is shown to capture the conditional distribution of these variables better than the commonly used autoregressive fractionally integrated moving average model. The forecasting performance of the new model is found to be, in general, superior to that of the set of volatility models recently considered by Andersen et al. (2003, Econometrica 71, 579--625) for the same data. Copyright 2006, Oxford University Press.

Suggested Citation

  • Markku Lanne, 2006. "A Mixture Multiplicative Error Model for Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 594-616.
  • Handle: RePEc:oup:jfinec:v:4:y:2006:i:4:p:594-616
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    1. Meitz, Mika & Saikkonen, Pentti, 2008. "Ergodicity, Mixing, And Existence Of Moments Of A Class Of Markov Models With Applications To Garch And Acd Models," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1291-1320, October.
    2. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 3-27.
    3. Giot, Pierre & Laurent, Sebastien, 2004. "Modelling daily Value-at-Risk using realized volatility and ARCH type models," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 379-398, June.
    4. Bos, Charles S. & Franses, Philip Hans & Ooms, Marius, 2002. "Inflation, forecast intervals and long memory regression models," International Journal of Forecasting, Elsevier, vol. 18(2), pages 243-264.
    5. Morana, Claudio & Beltratti, Andrea, 2004. "Structural change and long-range dependence in volatility of exchange rates: either, neither or both?," Journal of Empirical Finance, Elsevier, vol. 11(5), pages 629-658, December.
    6. Pong, Shiuyan & Shackleton, Mark B. & Taylor, Stephen J. & Xu, Xinzhong, 2004. "Forecasting currency volatility: A comparison of implied volatilities and AR(FI)MA models," Journal of Banking & Finance, Elsevier, vol. 28(10), pages 2541-2563, October.
    7. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    8. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    9. John M. Maheu & Thomas H. McCurdy, 2002. "Nonlinear Features of Realized FX Volatility," The Review of Economics and Statistics, MIT Press, pages 668-681.
    10. Manganelli, Simone, 2005. "Duration, volume and volatility impact of trades," Journal of Financial Markets, Elsevier, vol. 8(4), pages 377-399, November.
    11. Koopman, Siem Jan & Jungbacker, Borus & Hol, Eugenie, 2005. "Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 445-475, June.
    12. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-235, April.
    13. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    14. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
    15. Markus Haas, 2004. "Mixed Normal Conditional Heteroskedasticity," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 211-250.
    16. Danielsson, J. & Payne, R., 2002. "Real trading patterns and prices in spot foreign exchange markets," Journal of International Money and Finance, Elsevier, vol. 21(2), pages 203-222, April.
    17. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
    18. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    19. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    20. Bauwens, Luc & Giot, Pierre & Grammig, Joachim & Veredas, David, 2004. "A comparison of financial duration models via density forecasts," International Journal of Forecasting, Elsevier, vol. 20(4), pages 589-609.
    21. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range-Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    22. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
    23. Ole Barndorff-Nielsen & Neil Shephard, 2000. "Non-Gaussian OU based models and some of their uses in financial economics," OFRC Working Papers Series 2000mf01, Oxford Financial Research Centre.
    24. Chou, Ray Yeutien, 2005. "Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 561-582, June.
    25. De Luca Giovanni & Gallo Giampiero M., 2004. "Mixture Processes for Financial Intradaily Durations," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-20, May.
    26. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
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    Cited by:

    1. Chen, Ray-Bing & Chen, Ying & Härdle, Wolfgang K., 2014. "TVICA—Time varying independent component analysis and its application to financial data," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 95-109.
    2. Ng, F.C. & Li, W.K. & Yu, Philip L.H., 2016. "Diagnostic checking of the vector multiplicative error model," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 86-97.
    3. repec:eur:ejisjr:41 is not listed on IDEAS
    4. Christian T. Brownlees & Fabrizio Cipollini & Giampiero M. Gallo, 2011. "Multiplicative Error Models," Econometrics Working Papers Archive 2011_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", revised Apr 2011.
    5. Heejoon Han & Myung D. Park & Shen Zhang, 2015. "A Multiplicative Error Model with Heterogeneous Components for Forecasting Realized Volatility," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(3), pages 209-219, April.
    6. Caporin, Massimiliano & Rossi, Eduardo & Santucci de Magistris, Paolo, 2017. "Chasing volatility," Journal of Econometrics, Elsevier, vol. 198(1), pages 122-145.
    7. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(1), pages 89-121.
    8. Andres, Philipp, 2014. "Maximum likelihood estimates for positive valued dynamic score models; The DySco package," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 34-42.
    9. Giampiero M. Gallo & Edoardo Otranto, 2014. "Forecasting Realized Volatility with Changes of Regimes," Econometrics Working Papers Archive 2014_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", revised Feb 2014.
    10. Ahoniemi, Katja & Lanne, Markku, 2009. "Joint modeling of call and put implied volatility," International Journal of Forecasting, Elsevier, vol. 25(2), pages 239-258.
    11. Lanne, Markku, 2007. "Forecasting realized exchange rate volatility by decomposition," International Journal of Forecasting, Elsevier, vol. 23(2), pages 307-320.
    12. Giovanni De Luca & Giampiero Gallo, 2010. "A Time-varying Mixing Multiplicative Error Model for Realized Volatility," Econometrics Working Papers Archive wp2010_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    13. Lanne, Markku & Ahoniemi, Katja, 2008. "Implied Volatility with Time-Varying Regime Probabilities," MPRA Paper 23721, University Library of Munich, Germany.
    14. Gallo, Giampiero M. & Otranto, Edoardo, 2015. "Forecasting realized volatility with changing average levels," International Journal of Forecasting, Elsevier, vol. 31(3), pages 620-634.
    15. AUGUSTYNIAK, Maciej & BAUWENS, Luc & DUFAYS, Arnaud, 2016. "A New Approach to Volatility Modeling : The High-Dimensional Markov Model," CORE Discussion Papers 2016042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Christian T. Brownlees & Giampiero M. Gallo, 2010. "Comparison of Volatility Measures: a Risk Management Perspective," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 8(1), pages 29-56, Winter.
    17. Massimiliano Caporin & Eduardo Rossi & Paolo Santucci De Magistris, 2014. "Chasing Volatility. A Persistent Multiplicative Error Model With Jumps," "Marco Fanno" Working Papers 0186, Dipartimento di Scienze Economiche "Marco Fanno".
    18. Andrew J. Patton & Kevin Sheppard, 2015. "Good Volatility, Bad Volatility: Signed Jumps and The Persistence of Volatility," The Review of Economics and Statistics, MIT Press, vol. 97(3), pages 683-697, July.
    19. Markku Lanne, 2006. "Forecasting Realized Volatility by Decomposition," Economics Working Papers ECO2006/20, European University Institute.
    20. Preve, Daniel, 2015. "Linear programming-based estimators in nonnegative autoregression," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 225-234.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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