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On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential Equations

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  • A. S. Hurn
  • K. A. Lindsay
  • V. L. Martin

Abstract

A method for estimating the parameters of stochastic differential equations (SDEs) by simulated maximum likelihood is presented. This method is feasible whenever the underlying SDE is a Markov process. Estimates are compared to those generated by indirect inference, discrete and exact maximum likelihood. The technique is illustrated with reference to a one-factor model of the term structure of interest rates using 3-month US Treasury Bill data. Copyright 2003 Blackwell Publishing Ltd.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 24 (2003)
Issue (Month): 1 (01)
Pages: 45-63

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Handle: RePEc:bla:jtsera:v:24:y:2003:i:1:p:45-63

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References

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  1. Yacine Ait-Sahalia, 1995. "Nonparametric Pricing of Interest Rate Derivative Securities," NBER Working Papers 5345, National Bureau of Economic Research, Inc.
  2. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
  3. Pastorello, S. & Renault, E. & Touzi, N., 1995. "Statistical Inference for Random Variance Option Pricing," Papers 95.403, Toulouse - GREMAQ.
  4. Pagan, A.R. & Hall, A.D. & Martin, V., 1995. "Modelling the Term Structure," Papers 284, Australian National University - Department of Economics.
  5. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
  6. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  7. Eckhard Platen, 1999. "An Introduction to Numerical Methods for Stochastic Differential Equations," Research Paper Series 6, Quantitative Finance Research Centre, University of Technology, Sydney.
  8. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S85-118, Suppl. De.
  9. Elerian, O. & Chib, S. & Shephard, N., 1998. "Likelihood INference for Discretely Observed Non-linear Diffusions," Economics Papers 146, Economics Group, Nuffield College, University of Oxford.
  10. Michael J. Brennan and Eduardo S. Schwartz., 1979. "A Continuous-Time Approach to the Pricing of Bonds," Research Program in Finance Working Papers 85, University of California at Berkeley.
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Citations

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Cited by:
  1. Isambi Mbalawata & Simo Särkkä & Heikki Haario, 2013. "Parameter estimation in stochastic differential equations with Markov chain Monte Carlo and non-linear Kalman filtering," Computational Statistics, Springer, vol. 28(3), pages 1195-1223, June.
  2. Neil Shephard & Siddhartha Chib, 2004. "Likelihood based inference for diffusion driven models," Economics Series Working Papers 2004-FE-17, University of Oxford, Department of Economics.
  3. Stan Hurn & J.Jeisman & K.A. Lindsay, 2006. "Teaching an old dog new tricks: Improved estimation of the parameters of SDEs by numerical solution of the Fokker-Planck equation," Stan Hurn Discussion Papers 2006-01, School of Economics and Finance, Queensland University of Technology.
  4. Andrew D. Sanford & Gael Martin, 2004. "Bayesian Analysis of Continuous Time Models of the Australian Short Rate," Monash Econometrics and Business Statistics Working Papers 11/04, Monash University, Department of Econometrics and Business Statistics.
  5. John Stachurski & University of Melbourne, 2006. "Computing the Distributions of Economic Models via Simulation," Computing in Economics and Finance 2006 185, Society for Computational Economics.
  6. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
  7. Stan Hurn & J.Jeisman & K.A. Lindsay, 2006. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations. Working paper #2," NCER Working Paper Series 2, National Centre for Econometric Research.
  8. Kathleen Goffey & Andrew Worthington, 2002. "Motor Vehicle Usage Patterns in Australia: A Comparative Analysis of Driver, Vehicle & Purpose Characteristics for Household & Freight Travel," School of Economics and Finance Discussion Papers and Working Papers Series 117, School of Economics and Finance, Queensland University of Technology.
  9. J. Jimenez & R. Biscay & T. Ozaki, 2005. "Inference Methods for Discretely Observed Continuous-Time Stochastic Volatility Models: A Commented Overview," Asia-Pacific Financial Markets, Springer, vol. 12(2), pages 109-141, June.
  10. Stan Hurn & J.Jeisman & K.A. Lindsay, 2006. "Seeing the wood for the trees: A critical evaluation of methods to estimate the parameters of stochastic differential equations," Stan Hurn Discussion Papers 2006, School of Economics and Finance, Queensland University of Technology.
  11. A. Hurn & J. Jeisman & K. Lindsay, 2007. "Teaching an Old Dog New Tricks: Improved Estimation of the Parameters of Stochastic Differential Equations by Numerical Solution of the Fokker-Planck Equation," NCER Working Paper Series 9, National Centre for Econometric Research.

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