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Exact Maximum Likelihood Estimation of Observation-Driven Econometric Models

  • Francis X. Diebold
  • Til Schuermann

The possibility of exact maximum likelihood estimation of many observation-driven models remains an open question. Often only approximate maximum likelihood estimation is attempted, because the unconditional density needed for exact estimation is not known in closed form. Using simulation and nonparametric density estimation techniques that facilitate empirical likelihood evaluation, we develop an exact maximum likelihood procedure. We provide an illustrative application to the estimation of ARCH models, in which we compare the sampling properties of the exact estimator to those of several competitors. We find that, especially in situations of small samples and high persistence, efficiency gains are obtained. We conclude with a discussion of directions for future research, including application of our methods to panel data models.

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File URL: http://www.nber.org/papers/t0194.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0194.

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Date of creation: Apr 1996
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Publication status: published as Mariano, R.S., T. Schuermann, and M. Weeks (eds.) Simulation-Based inference in Econometrics: Methods and Applications. New York: Cambridge University Press, 2008.
Handle: RePEc:nbr:nberte:0194
Note: EFG
Contact details of provider: Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.
Phone: 617-868-3900
Web page: http://www.nber.org
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  1. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  2. Diebold & Lopez, . "Modeling Volatility Dynamics," Home Pages _062, University of Pennsylvania.
  3. Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
  4. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  5. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  6. Bhargava, Alok & Sargan, J D, 1983. "Estimating Dynamic Random Effects Models from Panel Data Covering Short Time Periods," Econometrica, Econometric Society, vol. 51(6), pages 1635-59, November.
  7. Beach, Charles M & MacKinnon, James G, 1978. "A Maximum Likelihood Procedure for Regression with Autocorrelated Errors," Econometrica, Econometric Society, vol. 46(1), pages 51-58, January.
  8. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
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