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Nonparametric specification testing for continuous-time models with application to spot interest rates

  • Hong, Yongmiao
  • Li, Haitao

We propose two nonparametric transition density-based speciþcation tests for continuous-time diffusion models. In contrast to marginal density as used in the literature, transition density can capture the full dynamics of a diffusion process, and in particular, can distinguish processes with the same marginal density but different transition densities. To address the concerns of the þnite sample performance of nonparametric methods in the literature, we introduce an appropriate data transformation and correct the boundary bias of kernel estimators. As a result, our tests are robust to persistent dependence in data and provide reliable inferences for sample sizes often encountered in empirical þnance. Simulation studies show that our tests have reasonable size and good power against a variety of alternatives in þnite samples even for data with highly persistent dependence. Besides the single-factor diffusion models, our tests can be applied to a broad class of dynamic economic models, such as discrete time series models, time-inhomogeneous diffusion models, stochastic volatility models, jump-diffusion models, and multi-factor term structure models. When applied to daily Eurodollar interest rates, our tests overwhelmingly reject some popular spot rate models, including those with nonlinear drifts that some existing tests can not reject after correcting size distortions. We þnd that models with nonlinear drifts do not signiþcantly improve the goodness-of-þt, and the main source of model inadequacy seems to be the violation of the Markov assumption. We also þnd that GARCH, regime switching and jump diffusion models perform signiþcantly better than single-factor diffusion models, although they are far from being adequate to fully capture the interest rate dynamics. Our study shows that nonparametric methods are a reliable and powerful tool for analyzing þnancial data.

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Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2002,32.

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Date of creation: 2002
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Handle: RePEc:zbw:sfb373:200232
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  1. 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.
  2. Chen, Song Xi & Härdle, Wolfgang & Kleinow, Torsten, 2000. "An empirical likelihood goodness-of-fit test for time series," SFB 373 Discussion Papers 2001,1, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  3. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
  4. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
  5. Ang, Andrew & Bekaert, Geert, 2002. "Regime Switches in Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 163-82, April.
  6. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606.
  7. Ola Elerian & Siddhartha Chib & Neil Shephard, 2000. "Likelihood inference for discretely observed non-linear diffusions," OFRC Working Papers Series 2000mf02, Oxford Financial Research Centre.
  8. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-52, July.
  9. David A. Chapman & Neil D. Pearson, 2000. "Is the Short Rate Drift Actually Nonlinear?," Journal of Finance, American Finance Association, vol. 55(1), pages 355-388, 02.
  10. Gray, Stephen F., 1996. "Modeling the conditional distribution of interest rates as a regime-switching process," Journal of Financial Economics, Elsevier, vol. 42(1), pages 27-62, September.
  11. Pritsker, Matt, 1998. "Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 449-87.
  12. Egorov, Alexei V. & Li, Haitao & Xu, Yuewu, 2003. "Maximum likelihood estimation of time-inhomogeneous diffusions," Journal of Econometrics, Elsevier, vol. 114(1), pages 107-139, May.
  13. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590.
  14. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
  15. Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(02), pages 235-254, June.
  16. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
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