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GARCH for Irregularly Spaced Financial Data: The ACD-GARCH Model

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Author Info
Eric Ghysels (Pennsylvania State University)
Joanna Jasiak (York University)

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Abstract

We develop a class of ARCH models for series sampled at unequal time intervals set by trade orquote arrivals. Our approach combines insights from the temporal aggregation for GARCH models discussed byDrost and Nijman (1993) and Drost and Werker (1996), and the autoregressive conditional duration model ofEngle and Russell (1996) proposed to model the spacing between consecutive financial transactions.The class of models introduced here will be called ACD-GARCH. It can be described as a random coefficientGARCH, or doubly stochastic GARCH, where the durations between transactions determine the parameterdynamics. The ACD-GARCH model becomes genuinely bivariate when past asset-return volatilities are allowedto affect transaction durations, and vice versa. Otherwise, the spacings between trades are consideredexogenous to the volatility dynamics. This assumption is required in a two-step estimation procedure. Thebivariate setup enables us to test for Granger causality between volatility and intratrade durations. Undergeneral conditions, we propose several Generalized Method of Moments (GMM) estimation procedures, somehaving a Quasi Maximum Likelihood Estimation (QMLE) interpretation. As illustration, we present anempirical study of the IBM 1993 tick-by-tick data. We find some evidence that volatility of IBM stock pricesGranger-causes intratrade durations. We also find that the persistence in GARCH drops dramatically onceintratrade durations are taken into account.

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Publisher Info
Article provided by Berkeley Electronic Press in its journal Studies in Nonlinear Dynamics & Econometrics.

Volume (Year): 2 (1998)
Issue (Month): 4 ()
Pages: 133-149
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Handle: RePEc:bep:sndecm:2:1998:4:133-149

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Keywords: tick-by-tick data subordinated processes duration models volatility

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Lamoureux, Christopher G & Lastrapes, William D, 1990. " Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects," Journal of Finance, American Finance Association, vol. 45(1), pages 221-29, March. [Downloadable!] (restricted)
  2. Ghysels, E. & Jasiak, J., 1994. "Stochastic Volatility and time Deformation: an Application of trading Volume and Leverage Effects," Cahiers de recherche 9403, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  3. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July. [Downloadable!] (restricted)
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  4. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  5. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July. [Downloadable!] (restricted)
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  6. Gourieroux, Christian & Jasiak, Joanna & Le Fol, Gaelle, 1999. "Intra-day market activity," Journal of Financial Markets, Elsevier, vol. 2(3), pages 193-226, August. [Downloadable!] (restricted)
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  7. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September. [Downloadable!] (restricted)
  8. Ghysels, E. & Gourieroux, C. & Jasiak, J., 1995. "Market Time and Asset Price Movements: Theory and Estimation," Cahiers de recherche 9536, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  9. Francis X. Diebold & Jose A. Lopez, 1995. "Modeling volatility dynamics," Research Paper 9522, Federal Reserve Bank of New York. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Andrea Beltratti & Andrea Consiglio & Stavros A. Zenios, 1998. "Scenario Modeling for the Management of International Bond Portfolios," Center for Financial Institutions Working Papers 98-20, Wharton School Center for Financial Institutions, University of Pennsylvania. [Downloadable!]
  2. Joel Hasbrouck, 1999. "Trading Fast and Slow: Security Market Events in Real Time," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-012, New York University, Leonard N. Stern School of Business-. [Downloadable!]
  3. Werker, B. & Meddahi, N. & Renault, E., 2003. "Garch and irregularly spaced data," Discussion Paper 27, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  4. Georges Dionne & Pierre Duchesne & Maria Pacurar, 2005. "Intraday Value at Risk (IVaR) Using Tick-by-Tick Data with Application to the Toronto Stock Exchange," Cahiers de recherche 0533, CIRPEE. [Downloadable!]
  5. Kati-Jasmin Kosonen, 2003. "New Technologies and Innovation Capacity - Boosting Economic Transition Processes in the Less Favoured Regions," ERSA conference papers ersa03p112, European Regional Science Association. [Downloadable!]
  6. Christian Gourieroux & Joann Jasiak, 2001. "Dynamic Factor Models," Econometric Reviews, Taylor and Francis Journals, vol. 20(4), pages 385-424. [Downloadable!] (restricted)
    Other versions:
  7. Tina Hviid Rydberg & Neil Shephard, 2002. "Dynamics of trade-by-trade price movements: decomposition and models," Economics Papers 2002-W1, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
    Other versions:
  8. Nikolaus Hautsch & Winfried Pohlmeier, 2001. "Econometric Analysis of Financial Transaction Data: Pitfalls and Opportunities," CoFE Discussion Paper 01-05, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  9. Wing Lon NG, 2004. "Duration and Order Type Clusters," Econometric Society 2004 Australasian Meetings 272, Econometric Society. [Downloadable!]
  10. Rohit Deo & Mengchen Hsieh & Clifford Hurvich, 2005. "Tracing the Source of Long Memory in Volatility," Econometrics 0501005, EconWPA. [Downloadable!]
  11. Wing Lon NG, 2004. "Duration and Order Type Clusters," Econometric Society 2004 Far Eastern Meetings 730, Econometric Society. [Downloadable!]
  12. Luc, BAUWENS & Nikolaus, HAUTSCH, 2006. "Modelling Financial High Frequency Data Using Point Processes," Université catholique de Louvain, Département des Sciences Economiques Working Paper 2006039, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]
    Other versions:
  13. Frank Gerhard & Nikolaus Hautsch, 1999. "Volatility Estimation on the Basis of Price Intensities," CoFE Discussion Paper 99-19, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
    Other versions:
  14. Grammig, Joachim & Fernandes, Marcelo, 2003. "Nonparametric specification tests for conditional duration models," Economics Working Papers (Ensaios Economicos da EPGE) 502, Graduate School of Economics, Getulio Vargas Foundation (Brazil). [Downloadable!]
    Other versions:
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