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A Simple R-Estimation Method for Semiparametric Duration Models

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  • Marc Hallin
  • Davide La Vecchia

Abstract

Modeling nonnegative financial variables (e.g. durations between trades, traded volumes or asset volatilities) is central to a number of studies across financial econometrics, and, despite the efforts, still poses several statistical challenges. Among them, the efficiency aspects of semiparametric estimation. In this paper, we concentrate on estimation problems in Autoregressive Conditional Duration (ACD) models with unspecified innovation densities. Exponential quasi-likelihood estimators (QMLE) are the usual practice in that context. The efficiency of those QMLEs (the only Fisher-consistent QMLEs) unfortunately rapidly deteriorates away from the reference exponential density—a phenomenon that has been emphasized earlier by Drost and Werker (2003), who propose various semiparametrically efficient procedures to palliate that phenomenon. Those procedures rely on a general semiparametric approach which typically requires kernel estimation of the underlying innovation density. We propose rank-based estimators (R-estimators) as a substitute. Just as the QMLE, R-estimators remain root-n consistent irrespective of the underlying density, and rely on the choice of a reference density under which they achieve semiparametric efficiency; that density, however, needs not be the exponential one. Contrary to the semiparametric estimators proposed by Drost and Werker (2003), R-estimators neither require tangent space calculations nor kernel-based density estimation. Numerical results moreover indicate that R-estimators based on exponential reference densities uniformly outperform the exponential QMLE under such families of innovations as the Weibull or Burr densities. A real data example about modeling the price range of the Swiss stock market index concludes the paper.

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  • Marc Hallin & Davide La Vecchia, 2017. "A Simple R-Estimation Method for Semiparametric Duration Models," Working Papers ECARES ECARES 2017-01, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2013/243446
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    1. Mukherjee, Kanchan & Bai, Z. D., 2002. "R-estimation in Autoregression with Square-Integrable Score Function," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 167-186, April.
    2. Marc Hallin & Madan Lal Puri, 1994. "Aligned rank tests for linear models with autocorrelated errors," ULB Institutional Repository 2013/2045, ULB -- Universite Libre de Bruxelles.
    3. Marc Hallin & Jean-François Ingenbleek & Madan Lal Puri, 1984. "Linear serial rank tests for randomness against ARMA alternatives," ULB Institutional Repository 2013/2167, ULB -- Universite Libre de Bruxelles.
    4. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    5. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1994. "Adaptive estimation in time-series models," Discussion Paper 1994-88, Tilburg University, Center for Economic Research.
    6. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    7. Marc Hallin & Youssef Benghabrit, 1996. "Rank-based tests for autoregressive against bilinear serial dependence," ULB Institutional Repository 2013/2057, ULB -- Universite Libre de Bruxelles.
    8. Andrews, Beth, 2012. "Rank-Based Estimation For Garch Processes," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1037-1064, October.
    9. Fernandes, Marcelo & Grammig, Joachim, 2006. "A family of autoregressive conditional duration models," Journal of Econometrics, Elsevier, vol. 130(1), pages 1-23, January.
    10. Beth Andrews, 2008. "Rank‐based estimation for autoregressive moving average time series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 51-73, January.
    11. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    12. 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.
    13. Biais, Bruno & Foucault, Thierry & Moinas, Sophie, 2015. "Equilibrium fast trading," Journal of Financial Economics, Elsevier, vol. 116(2), pages 292-313.
    14. Dufour, Jean-Marie & Roy, Roch, 1985. "Some robust exact results on sample autocorrelations and tests of randomness," Journal of Econometrics, Elsevier, vol. 29(3), pages 257-273, September.
    15. Hallin, Marc & van den Akker, Ramon & Werker, Bas J.M., 2016. "Semiparametric error-correction models for cointegration with trends: Pseudo-Gaussian and optimal rank-based tests of the cointegration rank," Journal of Econometrics, Elsevier, vol. 190(1), pages 46-61.
    16. Manganelli, Simone, 2005. "Duration, volume and volatility impact of trades," Journal of Financial Markets, Elsevier, vol. 8(4), pages 377-399, November.
    17. Marc Hallin & Bas Werker, 2003. "Semiparametric efficiency, distribution-freeness, and invariance," ULB Institutional Repository 2013/2119, ULB -- Universite Libre de Bruxelles.
    18. Martens, Martin & van Dijk, Dick, 2007. "Measuring volatility with the realized range," Journal of Econometrics, Elsevier, vol. 138(1), pages 181-207, May.
    19. repec:ulb:ulbeco:2013/127941 is not listed on IDEAS
    20. Alfonso Dufour & Robert F. Engle, 2000. "Time and the Price Impact of a Trade," Journal of Finance, American Finance Association, vol. 55(6), pages 2467-2498, December.
    21. Dufour, J.M., 1979. "Rank Tests for Serial Dependence," Cahiers de recherche 7815, Universite de Montreal, Departement de sciences economiques.
    22. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
    23. Marc Hallin & Ramon van den Akker & Bas Werker, 2009. "A class of Simple Semiparametrically Efficient Rank-Based Unit Root Tests," Working Papers ECARES 2009_001, ULB -- Universite Libre de Bruxelles.
    24. Kulan Ranasinghe & Mervyn J. Silvapulle, 2011. "Estimation Under Inequality Constraints: Semiparametric Estimation of Conditional Duration Models," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 359-378, August.
    25. Drost, Feike C & Werker, Bas J M, 2004. "Semiparametric Duration Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 40-50, January.
    26. Marc Hallin, 1994. "On the Pitman nonadmissibility of correlogram-based time series methods," ULB Institutional Repository 2013/2049, ULB -- Universite Libre de Bruxelles.
    27. Marc Hallin & Chintan Mehta, 2015. "R -Estimation for Asymmetric Independent Component Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 218-232, March.
    28. Hallin, Marc & Ingenbleek, Jean-Francois & Puri, Madan L., 1989. "Asymptotically most powerful rank tests for multivariate randomness against serial dependence," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 34-71, July.
    29. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    30. Hallin, Marc & Paindaveine, Davy, 2005. "Affine-invariant aligned rank tests for the multivariate general linear model with VARMA errors," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 122-163, March.
    31. Kunitomo, Naoto, 1992. "Improving the Parkinson Method of Estimating Security Price Volatilities," The Journal of Business, University of Chicago Press, vol. 65(2), pages 295-302, April.
    32. Ruey S. Tsay, 2009. "Autoregressive Conditional Duration Models," Palgrave Macmillan Books, in: Terence C. Mills & Kerry Patterson (ed.), Palgrave Handbook of Econometrics, chapter 21, pages 1004-1024, Palgrave Macmillan.
    33. Jean‐Marie Dufour, 1981. "Rank Tests For Serial Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 2(3), pages 117-128, May.
    34. Maria Pacurar, 2008. "Autoregressive Conditional Duration Models In Finance: A Survey Of The Theoretical And Empirical Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 22(4), pages 711-751, September.
    35. Andreou, Elena & Werker, Bas J.M., 2015. "Residual-based rank specification tests for AR–GARCH type models," Journal of Econometrics, Elsevier, vol. 185(2), pages 305-331.
    36. Hasbrouck, Joel, 2007. "Empirical Market Microstructure: The Institutions, Economics, and Econometrics of Securities Trading," OUP Catalogue, Oxford University Press, number 9780195301649, November.
    37. Marc Hallin & Davide La Vecchia, 2014. "Semiparametrically Efficient R-Estimation for Dynamic Location-Scale Models," Working Papers ECARES ECARES 2014-45, ULB -- Universite Libre de Bruxelles.
    38. Meitz, Mika & Terasvirta, Timo, 2006. "Evaluating Models of Autoregressive Conditional Duration," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 104-124, January.
    39. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
    40. Marc Hallin, 2017. "On Distribution and Quantile Functions, Ranks and Signs in R_d," Working Papers ECARES ECARES 2017-34, ULB -- Universite Libre de Bruxelles.
    41. 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.
    42. Dufour, J.M. & Hallin, M., 1986. "Tests Non Parametriques Optimaux Pour une Autoregression D'ordre Un," Cahiers de recherche 8652, Universite de Montreal, Departement de sciences economiques.
    43. Hallin, M. & Puri, M. L., 1994. "Aligned Rank Tests for Linear Models with Autocorrelated Error Terms," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 175-237, August.
    44. Marc Hallin & Davide La Vecchia & H Liu, 2019. "Center-Outward R-Estimation for Semiparametric VARMA Models," Working Papers ECARES 2019-25, ULB -- Universite Libre de Bruxelles.
    45. Marc Hallin & Youssef Benghabrit, 1992. "Optimal rank-based tests against first-order superdiagonal bilinear dependence," ULB Institutional Repository 2013/2039, ULB -- Universite Libre de Bruxelles.
    46. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    47. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
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    1. Marc Hallin & Davide La Vecchia & H Liu, 2019. "Center-Outward R-Estimation for Semiparametric VARMA Models," Working Papers ECARES 2019-25, ULB -- Universite Libre de Bruxelles.

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    More about this item

    Keywords

    efficiency; irregularly spaced data; quasi-likelihood; ranks; local asymptotic normality;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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