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Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data

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  • Andrew W. Lo

Abstract

In this paper, we consider the parametric estimation problem for continuous time stochastic processes described by general first-order nonlinear stochastic differential equations of the Ito type. We characterize the likelihood function of a discretely-sampled set of observations as the solution to a functional partial differential equation. The consistency and asymptotic normality of the maximum likelihood estimators are explored, and several illustrative examples are provided.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0059.

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Date of creation: Aug 1986
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Publication status: published as Econometric Theory, vol. 4, 1988, pp. 231-247
Handle: RePEc:nbr:nberte:0059

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  1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  2. Lars Peter Hansen & Thomas J. Sargent, 1982. "Formulating and estimating continuous time rational expectations models," Staff Report, Federal Reserve Bank of Minneapolis 75, Federal Reserve Bank of Minneapolis.
  3. Harrison, J Michael & Pitbladdo, Richard & Schaefer, Stephen M, 1984. "Continuous Price Processes in Frictionless Markets Have Infinite Variation," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 57(3), pages 353-65, July.
  4. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 363-84, March.
  5. Pierre Perron & Robert J. Shiller, 1984. "Testing the Random Walk Hypothesis: Power Versus Frequency of Observation," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 732, Cowles Foundation for Research in Economics, Yale University.
  6. Grossman, S J & Melino, Angelo & Shiller, Robert J, 1987. "Estimating the Continuous-Time Consumption-Based Asset-Pricing Model," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 5(3), pages 315-27, July.
  7. Harvey, A. C. & Stock, James H., 1985. "The Estimation of Higher-Order Continuous Time Autoregressive Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 1(01), pages 97-117, April.
  8. Marsh, Terry A & Rosenfeld, Eric R, 1983. " Stochastic Processes for Interest Rates and Equilibrium Bond Prices," Journal of Finance, American Finance Association, American Finance Association, vol. 38(2), pages 635-46, May.
  9. Abel, Andrew B, 1983. "Optimal Investment under Uncertainty," American Economic Review, American Economic Association, American Economic Association, vol. 73(1), pages 228-33, March.
  10. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, Econometric Society, vol. 39(3), pages 545-63, May.
  11. Ball, Clifford A & Torous, Walter N, 1985. " On Jumps in Common Stock Prices and Their Impact on Call Option Pricing," Journal of Finance, American Finance Association, American Finance Association, vol. 40(1), pages 155-73, March.
  12. Phillips, P C B, 1972. "The Structural Estimation of a Stochastic Differential Equation System," Econometrica, Econometric Society, Econometric Society, vol. 40(6), pages 1021-41, November.
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