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Likelihood based inference for diffusion driven models

Author

Listed:
  • Neil Shephard
  • Siddhartha Chib
  • Olin School of Business
  • Washington University
  • Michael K. Pitt
  • Department of Economics
  • University of Warwick

Abstract

This paper provides methods for carrying out likelihood based inference for diffusion driven models, for example discretely observed multivariate diffusions, continuous time stochastic volatility models and counting process models. The diffusions can potentially be non-stationary. Although our methods are sampling based, making use of Markov chain Monte Carlo methods to sample the posterior distribution of the relevant unknowns, our general strategies and details are different from previous work along these lines. The methods we develop are simple to implement and simulation efficient. Importantly, unlike previous methods, the performance of our technique is not worsened, in fact it improves, as the degree of latent augmentation is increased to reduce the bias of the Euler approximation. In addition, our method is not subject to a degeneracy that afflicts previous techniques when the degree of latent augmentation is increased. We also discuss issues of model choice, model checking and filtering. The techniques and ideas are applied to both simulated and real data.

Suggested Citation

  • Neil Shephard & Siddhartha Chib & Olin School of Business & Washington University & Michael K. Pitt & Department of Economics & University of Warwick, 2004. "Likelihood based inference for diffusion driven models," Economics Series Working Papers 2004-FE-17, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:2004-fe-17
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    Citations

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    Cited by:

    1. Fernández-Villaverde, Jesús & Guerrón-Quintana, Pablo & Rubio-Ramírez, Juan F., 2015. "Estimating dynamic equilibrium models with stochastic volatility," Journal of Econometrics, Elsevier, vol. 185(1), pages 216-229.
    2. Aliu, A. Hassan & Abiodun A. A. & Ipinyomi R.A., 2017. "Statistical Inference for Discretely Observed Diffusion Epidemic Models," International Journal of Mathematics Research, Conscientia Beam, vol. 6(1), pages 29-35.
    3. Nicolas Chopin & Mathieu Gerber, 2017. "Sequential quasi-Monte Carlo: Introduction for Non-Experts, Dimension Reduction, Application to Partly Observed Diffusion Processes," Working Papers 2017-35, Center for Research in Economics and Statistics.
    4. Marcin Mider & Paul A. Jenkins & Murray Pollock & Gareth O. Roberts, 2022. "The Computational Cost of Blocking for Sampling Discretely Observed Diffusions," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3007-3027, December.
    5. Matthew M. Graham & Alexandre H. Thiery & Alexandros Beskos, 2022. "Manifold Markov chain Monte Carlo methods for Bayesian inference in diffusion models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1229-1256, September.
    6. Osnat Stramer & Jun Yan, 2007. "Asymptotics of an Efficient Monte Carlo Estimation for the Transition Density of Diffusion Processes," Methodology and Computing in Applied Probability, Springer, vol. 9(4), pages 483-496, December.
    7. repec:wyi:journl:002117 is not listed on IDEAS
    8. Martin J. Lenardon & Anna Amirdjanova, 2006. "Interaction between stock indices via changepoint analysis," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 22(5‐6), pages 573-586, September.
    9. repec:wyi:journl:002142 is not listed on IDEAS
    10. Peavoy, Daniel & Franzke, Christian L.E. & Roberts, Gareth O., 2015. "Systematic physics constrained parameter estimation of stochastic differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 182-199.
    11. S. C. Kou & Benjamin P. Olding & Martin Lysy & Jun S. Liu, 2012. "A Multiresolution Method for Parameter Estimation of Diffusion Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1558-1574, December.

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