IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

GARCH for Irregularly Spaced Data: The ACD-GARCH Model

  • Eric Ghysels
  • Joanna Jasiak

We develop a class of ARCH models for series sampled at unequal time intervals set by trade or quote arrivals. Our approach combines insights from the temporal aggregation for GARCH models discussed by Drost and Nijman (1993) and Drost and Werker (1994), and the autoregressive conditional duration model of Engle and Russell (1996) proposed to model the spacing between consecutive financial transactions. The class of models we introduce here will be called ACD-GARCH. It can be described as a random coefficient GARCH, or doubly stochastic GARCH, where the durations between transactions determine the parameter dynamics. The ACD-GARCH model becomes genuinely bivariate when past asset return volatilities are allowed to affect transaction durations and vice versa. Otherwise the spacings between trades are considered exogenous to the volatility dynamics. This assumption is required in a two-step estimation procedure. The bivariate setup enables us to test for Granger causality between volatility and intra-trade durations. Under general conditions we propose several GMM estimation procedures, some having a QMLE interpretation. As illustration we present an empirical study of the IBM 1993 tick-by-tick data. We find that volatility of IBM stock prices Granger causes intra-trade durations. We also find that the persistence in GARCH drops dramatically once intra-trade durations are taken into account. Nous développons une classe de modèles ARCH pour les séries temporelles échantillonnées à intervalles inégaux comme des observations liées à des transactions de marché. Notre approche est fondée sur la méthode d'aggrégation temporelle pour les modèles ARCH de Drost et Nijman (1993) et de Drost et Werker (1994), et d'autre part sur le modèle autorégressif des moyennes conditionnelles des durées entre les transactions financières de Engle et Russell (1996). La classe de modèles présentée ici est nommée ACD-GARCH. Ce type de modèles peut être défini comme un GARCH aux coefficients aléatoires où la durée entre les transactions détermine la dynamique des paramètres. Le ACD-GARCH devient un modèle bivarié quand sa formation admet les interactions entre les volatilités des rendements passés et les durées, et vice-versa. Sinon, la série de durées est considérée exogène par rapport au processus de volatilité. Cette condition est préalable à l'estimation du modèle ACD-GARCH en deux étapes. La spécification bivariée nous permet de tester l'existence de la causalité de type Granger entre les volatilités et les durées. Sous conditions générales, diverses procédures d'estimation par la méthode de moments généralisés sont considérées, dont certaines fournissent les estimateurs, à la fois de type GMM et de type QMLE. Pour ce qui est des applications, nous présentons une étude empirique basée sur les données de transactions du titre IBM en 1993. Nos résultats indiquent que la volatilité des rendements sur les prix d'actions de IBM cause, au sens de Granger, les durées entre les transactions. Nous observons aussi que la persistance du processus GARCH diminue fortement quand on introduit les durées dans la formulation du modèle.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.cirano.qc.ca/files/publications/97s-06.pdf
Download Restriction: no

Paper provided by CIRANO in its series CIRANO Working Papers with number 97s-06.

as
in new window

Length: 31 pages
Date of creation: 01 Feb 1997
Date of revision:
Handle: RePEc:cir:cirwor:97s-06
Contact details of provider: Postal: 1130 rue Sherbrooke Ouest, suite 1400, Montréal, Quéc, H3A 2M8
Phone: (514) 985-4000
Fax: (514) 985-4039
Web page: http://www.cirano.qc.ca/
Email:


More information through EDIRC

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.:

as in new window
  1. Ghysels, E. & Jasiak, J., 1994. "Stochastic Volatility and time Deformation: An Application of trading Volume and Leverage Effects," Cahiers de recherche 9403, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers 9240, Tilburg - Center for Economic Research.
  3. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
  4. 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.
  5. Palm, Franz C & Nijman, Theo E, 1984. "Missing Observations in the Dynamic Regression Model," Econometrica, Econometric Society, vol. 52(6), pages 1415-35, November.
  6. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  7. Cheung, Yin-Wong & Ng, Lilian K., 1996. "A causality-in-variance test and its application to financial market prices," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 33-48.
  8. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  9. Francis X. Diebold & Jose A. Lopez, 1995. "Modeling volatility dynamics," Research Paper 9522, Federal Reserve Bank of New York.
  10. Marcel Boyer, 1997. "Competition and Access in Telecoms: ECPR, Global Price Cap, and Auctions," CIRANO Working Papers 97s-03, CIRANO.
  11. Nijman, T.E. & Palm, F.C., 1987. "Predictive accuracy gain from disaggregate sampling in ARIMA-models," Research Memorandum FEW 273, Tilburg University, School of Economics and Management.
  12. repec:ner:tilbur:urn:nbn:nl:ui:12-153276 is not listed on IDEAS
  13. Robert F. Engle & Jeffrey R. Russell, 1994. "Forecasting Transaction Rates: The Autoregressive Conditional Duration Model," NBER Working Papers 4966, National Bureau of Economic Research, Inc.
  14. repec:ner:tilbur:urn:nbn:nl:ui:12-153273 is not listed on IDEAS
  15. Bollerslev, T. & Ghysels, E., 1994. "Periodic Autoregressive Conditional Heteroskedasticity," Cahiers de recherche 9408, Universite de Montreal, Departement de sciences economiques.
  16. Eric Ghysels & Christian Gouriéroux & Joanna Jasiak, 1995. "Market Time and Asset Price Movements Theory and Estimation," CIRANO Working Papers 95s-32, CIRANO.
  17. repec:ner:tilbur:urn:nbn:nl:ui:12-153295 is not listed on IDEAS
  18. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
  19. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  20. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  21. Eric Ghysels & Christian Gouriéroux & Joanna Jasiak, 1995. "Trading Patterns, Time Deformation and Stochastic Volatility in Foreign Exchange Markets," CIRANO Working Papers 95s-42, CIRANO.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:cir:cirwor:97s-06. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Webmaster)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.