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On identification of continuous time stochastic processes

  • Jeremy Berkowitz
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    In this note we delineate conditions under which continuous time stochastic processes can be identified from discrete data. The identification problem is approached in a novel way. The distribution of the observed stochastic process is expressed as the underlying true distribution, f, transformed by some operator, T. Using a generalization of the Taylor series expansion, the transformed function T f can often be expressed as a linear combination of the original function f. By combining the information across a large number of such transformations, the original measurable function of interest can be recovered.

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    File URL: http://www.federalreserve.gov/pubs/feds/2000/200007/200007abs.html
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    File URL: http://www.federalreserve.gov/pubs/feds/2000/200007/200007pap.pdf
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    Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2000-07.

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    Date of creation: 2000
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    Handle: RePEc:fip:fedgfe:2000-07
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    1. Darrell Duffie & Kenneth J. Singleton, 1990. "Simulated Moments Estimation of Markov Models of Asset Prices," NBER Technical Working Papers 0087, National Bureau of Economic Research, Inc.
    2. Lars Peter Hansen & Thomas J. Sargent, 1981. "The dimensionality of the aliasing problem in models with rational spectral densities," Staff Report 72, Federal Reserve Bank of Minneapolis.
    3. Hansen, Lars Peter & Alexandre Scheinkman, Jose & Touzi, Nizar, 1998. "Spectral methods for identifying scalar diffusions," Journal of Econometrics, Elsevier, vol. 86(1), pages 1-32, June.
    4. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    5. Andrew W. Lo, . "Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data," Rodney L. White Center for Financial Research Working Papers 15-86, Wharton School Rodney L. White Center for Financial Research.
    6. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May.
    7. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
    8. 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.
    9. Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc.
    10. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
    11. Phillips, P. C. B., 1973. "The problem of identification in finite parameter continuous time models," Journal of Econometrics, Elsevier, vol. 1(4), pages 351-362, December.
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