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

  • Hurvich, Cliiford
  • Wang, Yi

We propose a new transaction-level bivariate log-price model, which yields fractional or standard cointegration. To the best of our knowledge, all existing models for cointegration require the choice of a fixed sampling frequency Delta t. By contrast, our proposed model is constructed at the transaction level, thus determining the properties of returns at all sampling frequencies. The two ingredients of our model are a Long Memory Stochastic Duration process for the waiting times tau(k) between trades, and a pair of stationary noise processes ( e(k) and eta(k) ) which determine the jump sizes in the pure-jump log-price process. The e(k), assumed to be iid Gaussian, produce a Martingale component in log prices. We assume that the microstructure noise eta(k) obeys a certain model with memory parameter d(eta) in (-1/2,0) (fractional cointegration case) or d(eta) = -1 (standard cointegration case). Our log-price model includes feedback between the shocks of the two series. This feedback yields cointegration, in that there exists a linear combination of the two components that reduces the memory parameter from 1 to 1+d(eta) in (0.5,1) and (0). Returns at sampling frequency Delta t are asymptotically uncorrelated at any fixed lag as Delta t increases. 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 several of the other parameters in our model. We present a data analysis, which provides evidence of fractional cointegration. We then consider special cases and generalizations of our model, mostly in simulation studies, to argue that the suitably-modified model is able to capture a variety of additional properties and stylized facts, including leverage, portfolio return autocorrelation due to nonsynchronous trading, Granger causality, and volatility feedback. 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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 1413.

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Date of creation: 04 Dec 2006
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Handle: RePEc:pra:mprapa:1413
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  1. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
  2. Perry, Philip R., 1985. "Portfolio Serial Correlation and Nonsynchronous Trading," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(04), pages 517-523, December.
  3. Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Wiley Blackwell, vol. 53(4), pages 473-95, August.
  4. Javier Hualde & Peter M Robinson, 2003. "Cointegration in Fractional Systems with Unkown Integration Orders," STICERD - Econometrics Paper Series /2003/449, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  5. Frijns, Bart & Schotman, Peter C, 2004. "Price Discovery in Tick Time," CEPR Discussion Papers 4456, C.E.P.R. Discussion Papers.
  6. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
  7. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous-time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323.
  8. Peter M Robinson & Yoshihiro Yajima, 2001. "Determination of Cointegrating Rank in Fractional Systems," STICERD - Econometrics Paper Series /2001/423, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  9. Chen, Willa W. & Hurvich, Clifford M., 2003. "Estimating fractional cointegration in the presence of polynomial trends," Journal of Econometrics, Elsevier, vol. 117(1), pages 95-121, November.
  10. 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.
  11. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
  12. Liu, Jun & Longstaff, Francis & Pan, Jun, 2001. "Dynamic Asset Allocation with Event Risk," University of California at Los Angeles, Anderson Graduate School of Management qt9fm6t5nb, Anderson Graduate School of Management, UCLA.
  13. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
  14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  15. D Marinucci & Peter M Robinson, 2001. "Narrow-Band Analysis of Nonstationary Processes," STICERD - Econometrics Paper Series /2001/421, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  16. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  17. Lee, Charles M C & Ready, Mark J, 1991. " Inferring Trade Direction from Intraday Data," Journal of Finance, American Finance Association, vol. 46(2), pages 733-46, June.
  18. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  19. Carol Alexander & Anca Dimitriu, 2005. "Indexing, cointegration and equity market regimes," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 10(3), pages 213-231.
  20. Peter M. Robinson & Javier Hualde, 2002. "Cointegration in Fractional Systems with Unknown Integration Orders," Faculty Working Papers 07/02, School of Economics and Business Administration, University of Navarra.
  21. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
  22. Clive G. Bowsher, 2005. "Modelling Security Market Events in Continuous Time: Intensity Based, Multivariate Point Process Models," Economics Papers 2005-W26, Economics Group, Nuffield College, University of Oxford.
  23. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September.
  24. 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.
  25. Francesc Marmol & Carlos Velasco, 2004. "Consistent Testing of Cointegrating Relationships," Econometrica, Econometric Society, vol. 72(6), pages 1809-1844, November.
  26. Andrew W. Lo & Craig A. MacKinlay, . "An Econometric Analysis of Nonsyschronous-Trading," Rodney L. White Center for Financial Research Working Papers 19-89, Wharton School Rodney L. White Center for Financial Research.
  27. Chen, Willa W. & Hurvich, Clifford M., 2003. "Semiparametric Estimation of Multivariate Fractional Cointegration," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 629-642, January.
  28. Atchison, Michael D & Butler, Kirt C & Simonds, Richard R, 1987. " Nonsynchronous Security Trading and Market Index Autocorrelation," Journal of Finance, American Finance Association, vol. 42(1), pages 111-18, March.
  29. Rohit Deo & Clifford Hurvich & Philippe Soulier & Yi Wang, 2005. "Propagation of Memory Parameter from Durations to Counts," Econometrics 0511010, EconWPA.
  30. Roll, Richard, 1984. " A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market," Journal of Finance, American Finance Association, vol. 39(4), pages 1127-39, September.
  31. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
  32. S. James Press, 1967. "A Compound Events Model for Security Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 317.
  33. 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 1173, Queen's University, Department of Economics.
  34. Kadlec, Gregory B & Patterson, Douglas M, 1999. "A Transactions Data Analysis of Nonsynchronous Trading," Review of Financial Studies, Society for Financial Studies, vol. 12(3), pages 609-30.
  35. Oomen, Roel C.A., 2006. "Properties of Realized Variance Under Alternative Sampling Schemes," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 219-237, April.
  36. D Marinucci & Peter Robinson, 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics 2015, London School of Economics and Political Science, LSE Library.
  37. Prigent, J.L., 1997. "Option Pricing with a General Market Point Process," Papers 9736, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  38. Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
  39. Offer Lieberman & Peter C.B. Phillips, 2006. "A Complete Asymptotic Series for the Autocovariance Function of a Long Memory Process," Cowles Foundation Discussion Papers 1586, Cowles Foundation for Research in Economics, Yale University.
  40. D Marinucci & Peter M. Robinson, 2001. "Semiparametric fractional cointegration analysis," LSE Research Online Documents on Economics 2269, London School of Economics and Political Science, LSE Library.
  41. Scholes, Myron & Williams, Joseph, 1977. "Estimating betas from nonsynchronous data," Journal of Financial Economics, Elsevier, vol. 5(3), pages 309-327, December.
  42. D. Marinucci & Peter M. Robinson, 2001. "Narrow-band analysis of nonstationary processes," LSE Research Online Documents on Economics 303, London School of Economics and Political Science, LSE Library.
  43. Comte, F., 1998. "Discrete and continuous time cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 207-226, November.
  44. Shanken, Jay, 1987. " Nonsynchronous Data and the Covariance-Factor Structure of Returns," Journal of Finance, American Finance Association, vol. 42(2), pages 221-31, June.
  45. Carlos Velasco, 2003. "Gaussian Semi-parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, 05.
  46. D Marinucci & Peter M Robinson, 2001. "Semiparametric Fractional Cointegration Analysis," STICERD - Econometrics Paper Series /2001/420, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  47. Willa Chen & Clifford Hurvich, 2004. "Semiparametric Estimation of Fractional Cointegrating Subspaces," Econometrics 0412007, EconWPA.
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