Advanced Search
MyIDEAS: Login to save this paper or follow this series

A Pure-Jump Transaction-Level Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects

Contents:

Author Info

  • Hurvich, Clifford
  • Wang, Yi

Abstract

We propose a new transaction-level bivariate log-price model, which yields fractional or standard cointegration. The model provides a link between market microstructure and lower-frequency observations. The two ingredients of our model are a Long Memory Stochastic Duration process for the waiting times between trades, and a pair of stationary noise processes which determine the jump sizes in the pure-jump log-price process. Our model includes feedback between the disturbances of the two log-price series at the transaction level, which induces standard or fractional cointegration for any fixed sampling interval. We prove that the cointegrating parameter can be consistently estimated by the ordinary least-squares estimator, and obtain a lower bound on the rate of convergence. We propose transaction-level method-of-moments estimators of the other parameters in our model and discuss the consistency of these estimators. We then use simulations to argue that suitably-modified versions of our model are able to capture a variety of additional properties and stylized facts, including leverage, and portfolio return autocorrelation due to nonsynchronous trading. The ability of the model to capture these effects stems in most cases from the fact that the model treats the (stochastic) intertrade durations in a fully endogenous way.

Download Info

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://mpra.ub.uni-muenchen.de/12575/
File Function: original version
Download Restriction: no

Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 12575.

as in new window
Length:
Date of creation: 05 Jan 2009
Date of revision:
Handle: RePEc:pra:mprapa:12575

Contact details of provider:
Postal: Schackstr. 4, D-80539 Munich, Germany
Phone: +49-(0)89-2180-2219
Fax: +49-(0)89-2180-3900
Web page: http://mpra.ub.uni-muenchen.de
More information through EDIRC

Related research

Keywords: Tick Time; Long Memory Stochastic Duration; Information Share;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

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. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 9613, Universite de Montreal, Departement de sciences economiques.
  2. Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 53(4), pages 473-95, August.
  3. Atchison, Michael D & Butler, Kirt C & Simonds, Richard R, 1987. " Nonsynchronous Security Trading and Market Index Autocorrelation," Journal of Finance, American Finance Association, American Finance Association, vol. 42(1), pages 111-18, March.
  4. Francesc Marmol & Carlos Velasco, 2004. "Consistent Testing of Cointegrating Relationships," Econometrica, Econometric Society, Econometric Society, vol. 72(6), pages 1809-1844, November.
  5. P. M. Robinson & J. Hualde, 2003. "Cointegration in Fractional Systems with Unknown Integration Orders," Econometrica, Econometric Society, Econometric Society, vol. 71(6), pages 1727-1766, November.
  6. Peter M Robinson & Yoshihiro Yajima, 2001. "Determination of Cointegrating Rank in Fractional Systems," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2001/423, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  7. Scholes, Myron & Williams, Joseph, 1977. "Estimating betas from nonsynchronous data," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(3), pages 309-327, December.
  8. Andrew W. Lo & A. Craig MacKinlay, 1991. "An Econometric Analysis of Nonsynchronous Trading," NBER Working Papers 2960, National Bureau of Economic Research, Inc.
  9. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous-time stochastic volatility models," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 8(4), pages 291-323.
  10. Frijns, Bart & Schotman, Peter, 2009. "Price discovery in tick time," Journal of Empirical Finance, Elsevier, Elsevier, vol. 16(5), pages 759-776, December.
  11. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 83(1-2), pages 325-348.
  12. Jun Liu & Francis A. Longstaff & Jun Pan, 2002. "Dynamic Asset Allocation With Event Risk," NBER Working Papers 9103, National Bureau of Economic Research, Inc.
  13. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
  14. D Marinucci & Peter Robinson, 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 2015, London School of Economics and Political Science, LSE Library.
  15. D. Marinucci & Peter M. Robinson, 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 303, London School of Economics and Political Science, LSE Library.
  16. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, Econometric Society, vol. 66(5), pages 1127-1162, September.
  17. Carol Alexander & Anca Dimitriu, 2005. "Indexing, cointegration and equity market regimes," International Journal of Finance & Economics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 10(3), pages 213-231.
  18. Rohit Deo & Clifford Hurvich & Philippe Soulier & Yi Wang, 2005. "Propagation of Memory Parameter from Durations to Counts," Econometrics, EconWPA 0511010, EconWPA.
  19. S. James Press, 1967. "A Compound Events Model for Security Prices," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 40, pages 317.
  20. Prigent, J.L., 1997. "Option Pricing with a General Market Point Process," Papers, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor. 9736, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  21. Torben G. Andersen & Tim Bollerslev & Per Frederiksen & Morten Ørregaard Nielsen, 2008. "Continuous-Time Models, Realized Volatilities, and Testable Distributional Implications for Daily Stock Returns," Working Papers, Queen's University, Department of Economics 1173, Queen's University, Department of Economics.
  22. Comte, F., 1998. "Discrete and continuous time cointegration," Journal of Econometrics, Elsevier, Elsevier, vol. 88(2), pages 207-226, November.
  23. Chen, Willa W. & Hurvich, Clifford M., 2003. "Estimating fractional cointegration in the presence of polynomial trends," Journal of Econometrics, Elsevier, Elsevier, vol. 117(1), pages 95-121, November.
  24. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, Econometric Society, vol. 41(1), pages 135-55, January.
  25. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, Elsevier, vol. 141(2), pages 876-912, December.
  26. Carlos Velasco, 2003. "Gaussian Semi-parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, 05.
  27. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, Elsevier, vol. 105(1), pages 225-247, November.
  28. Kadlec, Gregory B & Patterson, Douglas M, 1999. "A Transactions Data Analysis of Nonsynchronous Trading," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 12(3), pages 609-30.
  29. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 12(2-3), pages 231-254.
  30. Willa Chen & Clifford Hurvich, 2004. "Semiparametric Estimation of Fractional Cointegrating Subspaces," Econometrics, EconWPA 0412007, EconWPA.
  31. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, Econometric Society, vol. 59(6), pages 1551-80, November.
  32. Offer Lieberman & Peter C.B. Phillips, 2006. "A Complete Asymptotic Series for the Autocovariance Function of a Long Memory Process," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1586, Cowles Foundation for Research in Economics, Yale University.
  33. Chen, Willa W. & Hurvich, Clifford M., 2003. "Semiparametric Estimation of Multivariate Fractional Cointegration," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 98, pages 629-642, January.
  34. D Marinucci & Peter M Robinson, 2001. "Narrow-Band Analysis of Nonstationary Processes," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2001/421, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  35. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  36. Oomen, Roel C.A., 2006. "Properties of Realized Variance Under Alternative Sampling Schemes," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 24, pages 219-237, April.
  37. Michael Dueker & Richard Startz, 1998. "Maximum-Likelihood Estimation Of Fractional Cointegration With An Application To U.S. And Canadian Bond Rates," The Review of Economics and Statistics, MIT Press, vol. 80(3), pages 420-426, August.
  38. Perry, Philip R., 1985. "Portfolio Serial Correlation and Nonsynchronous Trading," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 20(04), pages 517-523, December.
  39. Shanken, Jay, 1987. " Nonsynchronous Data and the Covariance-Factor Structure of Returns," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 221-31, June.
  40. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, Econometric Society, vol. 55(5), pages 1035-56, September.
  41. Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, Elsevier, vol. 73(1), pages 101-149, July.
  42. D Marinucci & Peter M. Robinson, 2001. "Semiparametric fractional cointegration analysis," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 2269, London School of Economics and Political Science, LSE Library.
  43. Roll, Richard, 1984. " A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market," Journal of Finance, American Finance Association, American Finance Association, vol. 39(4), pages 1127-39, September.
  44. Lee, Charles M C & Ready, Mark J, 1991. " Inferring Trade Direction from Intraday Data," Journal of Finance, American Finance Association, American Finance Association, vol. 46(2), pages 733-46, June.
Full references (including those not matched with items on IDEAS)

Citations

Lists

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

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:12575. 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: (Ekkehart Schlicht).

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.