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On identification of continuous time stochastic processes

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  • Jeremy Berkowitz

Abstract

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.

Suggested Citation

  • Jeremy Berkowitz, 2000. "On identification of continuous time stochastic processes," Finance and Economics Discussion Series 2000-07, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgfe:2000-07
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    References listed on IDEAS

    as
    1. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    2. Lo, Andrew W., 1988. "Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data," Econometric Theory, Cambridge University Press, vol. 4(02), pages 231-247, August.
    3. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-952, July.
    4. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
    5. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
    6. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    7. Hansen, Lars Peter & Sargent, Thomas J, 1983. "The Dimensionality of the Aliasing Problem in Models with Rational Spectral Densities," Econometrica, Econometric Society, vol. 51(2), pages 377-387, March.
    8. 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.
    9. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
    10. 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.
    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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    Keywords

    Interest rates ; Asset pricing ; Econometric models;

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