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The Effects of Random and Discrete Sampling when Estimating Continuous--Time Diffusions

  • Yacine Ait--Sahalia

    ()

    (Princeton University, Princeton, U.S.A., and N.B.E.R)

  • Per A. Mykland

    ()

    (The University of Chicago, Chicago, IL, U.S.A.)

High--frequency financial data are not only discretely sampled in time but the time separating successive observations is often random. We analyze the consequences of this dual feature of the data when estimating a continuous--time model. In particular, we measure the additional effects of the randomness of the sampling intervals over and beyond those due to the discreteness of the data. We also examine the effect of simply ignoring the sampling randomness. We find that in many situations the randomness of the sampling has a larger impact than the discreteness of the data. Copyright The Econometric Society 2003.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 71 (2003)
Issue (Month): 2 (March)
Pages: 483-549

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Handle: RePEc:ecm:emetrp:v:71:y:2003:i:2:p:483-549
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  1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
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  3. Lars Peter Hansen & Jose Alexandre Scheinkman, 1993. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," NBER Technical Working Papers 0141, National Bureau of Economic Research, Inc.
  4. Florens, Jean-Pierre & Fougere, Denis, 1996. "Noncausality in Continuous Time," Econometrica, Econometric Society, vol. 64(5), pages 1195-1212, September.
  5. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-38, July.
  6. Yacine Ait-Sahalia, 1995. "Nonparametric Pricing of Interest Rate Derivative Securities," NBER Working Papers 5345, National Bureau of Economic Research, Inc.
  7. Hasbrouck, Joel, 1991. " Measuring the Information Content of Stock Trades," Journal of Finance, American Finance Association, vol. 46(1), pages 179-207, March.
  8. Robinson, P. M., 1977. "Estimation of a time series model from unequally spaced data," Stochastic Processes and their Applications, Elsevier, vol. 6(1), pages 9-24, November.
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  11. 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.
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  13. Gourieroux, Christian & Monfort, Alain & Renault, Eric & Trognon, Alain, 1987. "Generalised residuals," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 5-32.
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