Likelihood inference for discretely observed non-linear diffusions

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Likelihood inference for discretely observed non-linear diffusions

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Ola Elerian
Siddhartha Chib
Neil Shephard

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Abstract

This paper is concerned with the Bayesian estimation of non-linear stochastic differential equations when observations are discretely sampled. The estimation framework relies on the introduction of latent auxiliary data to complete the missing diffusion between each pair of measurements. Tuned Markov chain Monte Carlo (MCMC) methods based on the Metropolis-Hastings algorithm, in conjunction with the Euler-Maruyama discretization scheme, are used to sample the posterior distribution of the latent data and the model parameters. Techniques for computing the likelihood function, the marginal likelihood and diagnostic measures (all based on the MCMC output) are developed. Examples using simulated and real data are presented and discussed in detail.

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Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2000mf02.

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Date of creation: 2000
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Handle: RePEc:sbs:wpsefe:2000mf02

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Article
- Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-93, July.
Paper
- 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.

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)
Other versions:
- Gourieroux, C. & Monfort, A. & Renault, E., 1992. "Indirect Inference," Papers 92.279, Toulouse - GREMAQ.
- Gourieroux, C. & Monfort, A & Renault, E., 1992. "Indirect Inference," Papers 9215, Institut National de la Statistique et des Etudes Economiques-.
Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January. [Downloadable!] (restricted)
Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Blackwell Publishing, vol. 65(3), pages 361-93, July. [Downloadable!] (restricted)
Other versions:
- Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
- Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford. [Downloadable!]
- Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics 9610002, EconWPA. [Downloadable!]
Chib, Siddhartha & Greenberg, Edward & Winkelmann, Rainer, 1998. "Posterior simulation and Bayes factors in panel count data models," Journal of Econometrics, Elsevier, vol. 86(1), pages 33-54, June. [Downloadable!] (restricted)
Other versions:
- Siddhartha Chib & Edward Greenberg & Rainer Winkelmann, 1996. "Posterior Simulation and Bayes Factors in Panel Count Data Models," Econometrics 9608003, EconWPA, revised 25 Nov 1996. [Downloadable!]

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