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A minimum Hellinger distance estimator for stochastic differential equations: An application to statistical inference for continuous time interest rate models

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  • Giet, Ludovic
  • Lubrano, Michel

Abstract

A minimum disparity estimator minimizes a [phi]-divergence between the marginal density of a parametric model and its non-parametric estimate. This principle is applied to the estimation of stochastic differential equation models, choosing the Hellinger distance as particular [phi]-divergence. Under an hypothesis of stationarity, the parametric marginal density is provided by solving the Kolmogorov forward equation. A particular emphasis is put on the non-parametric estimation of the sample marginal density which has to take into account sample dependence and kurtosis. A new window size determination is provided. The classical estimator is presented alternatively as a distance minimizer and as a pseudo-likelihood maximizer. The latter presentation opens the way to Bayesian inference. The method is applied to continuous time models of the interest rate. In particular, various models are tested using alternatively tests and their results are discussed.

Suggested Citation

  • Giet, Ludovic & Lubrano, Michel, 2008. "A minimum Hellinger distance estimator for stochastic differential equations: An application to statistical inference for continuous time interest rate models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2945-2965, February.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:6:p:2945-2965
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    Cited by:

    1. Alessandro DE GREGORIO & Stefano Maria IACUS, 2011. "On a family of test statistics for discretely observed diffusion processes," Departmental Working Papers 2011-37, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    2. De Gregorio, A. & Iacus, S.M., 2013. "On a family of test statistics for discretely observed diffusion processes," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 292-316.
    3. Novriana Sumarti & Iman Gunadi, 2013. "Reserve Requirement Analysis using a Dynamical System of a Bank based on Monti-Klein model of Bank's Profit Function," Papers 1306.0468, arXiv.org.
    4. Alessandro DE GREGORIO & Stefano Maria IACUS, 2009. "Pseudo phi-divergence test statistics and multidimensional Ito processes," Departmental Working Papers 2009-48, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    5. Takada, Teruko, 2009. "Simulated minimum Hellinger distance estimation of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2390-2403, April.

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