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Accurate and robust indirect inference for diffusion models

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  • Veronika Czellar
  • Elvezio Ronchetti
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    Abstract

    Indirect inference (Smith, 1993; Gouriéroux, Monfort and Renault, 1993) is a simulation-based estimation method dealing with econometric models whose likelihood function is intractable. Typical examples are diffusion models described by stochastic differential equations. A potential problem that arises when estimating a diffusion model is the possible model misspecifcation which can lead to biased estimators and misleading test results. To correct the bias due to model misspecifcation, Genton and Ronchetti (2003) proposed robust indirect inference. The standard asymptotic approximation to the finite sample distribution of the robust indirect estimators and tests, however, can be very poor and can lead to misleading inference. To improve the finite sample accuracy, we propose in this paper an optimal choice of the auxiliary discretized model and a new test based on asymptotically equivalent M-estimators of the robust indirect estimators. We apply the robust indirect saddlepoint tests using an optimal choice of discretization to various contaminated diffusion models and we illustrate the gain in finite sample accuracy when using the new technique.

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    Bibliographic Info

    Paper provided by Institut d'Economie et Econométrie, Université de Genève in its series Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva with number 2008.01.

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    Length: 32 pages
    Date of creation: Aug 2008
    Date of revision:
    Handle: RePEc:gen:geneem:2008.01

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    Related research

    Keywords: indirect inference; M-estimators; influence function; robust statistics; saddlepoint approximations;

    This paper has been announced in the following NEP Reports:

    References

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    1. Czellar, Veronika & Karolyi, G. Andrew & Ronchetti, Elvezio, 2007. "Indirect robust estimation of the short-term interest rate process," Journal of Empirical Finance, Elsevier, vol. 14(4), pages 546-563, September.
    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. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    4. Gourieroux, C. & Monfort, A. & Renault, E., 1992. "Indirect Inference," Papers 92.279, Toulouse - GREMAQ.
    5. Robert C. Merton, 1980. "On Estimating the Expected Return on the Market: An Exploratory Investigation," NBER Working Papers 0444, National Bureau of Economic Research, Inc.
    6. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
    7. Ortelli, Claudio & Trojani, Fabio, 2005. "Robust efficient method of moments," Journal of Econometrics, Elsevier, vol. 128(1), pages 69-97, September.
    8. Smith, A A, Jr, 1993. "Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S63-84, Suppl. De.
    9. Broze, Laurence & Scaillet, Olivier & Zako an, Jean-Michel, 1998. "Quasi-Indirect Inference For Diffusion Processes," Econometric Theory, Cambridge University Press, vol. 14(02), pages 161-186, April.
    10. Knut Heggland & Arnoldo Frigessi, 2004. "Estimating functions in indirect inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 447-462.
    11. Genton, Marc G. & de Luna, Xavier, 2000. "Robust simulation-based estimation," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 253-259, July.
    12. Yacine Aït-Sahalia, 1999. "Transition Densities for Interest Rate and Other Nonlinear Diffusions," Journal of Finance, American Finance Association, vol. 54(4), pages 1361-1395, 08.
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