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Bootstrap Specification Tests for Diffusion Processes

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Author Info
Valentina Corradi () (Queen Mary, University of London)
Norman R. Swanson () (Rutgers University)

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Abstract

This paper introduces bootstrap specification tests for diffusion processes. In the one-dimensional case, the proposed test is closest to the non parametric test introduced by Ait-Sahalia (1996), in the sense that both procedures determine whether the drift and variance components of a particular continuous time model are correctly specified. However we compare cumulative distribution functions, while Ait-Sahalia compares probability densities. In the multidimensional and/or multifactor case, the proposed test is based on the comparison of empirical CDF of the actual data and the empirical CDF of the simulated data. The limiting distributions of both tests are functionals of zero mean Gaussian processes with covariance kernels that reflect data dependence and parameter estimation error (PEE). In order to obtain asymptotically valid critical values for the test, we use an empirical process version of the block bootstrap which properly accounts for the contribution of PEE. An example based on a simple version of Cox, Ingersol and Ross (1985) square root process is outlined and related Monte Carlo experiments are carried out. These experiments suggest that the test has good finite sample properties, even for samples as small as 400 observations when tests are formed using critical values constructed with as few as 100 bootstrap replications.

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Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 200321.

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Date of creation: 27 Oct 2003
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Handle: RePEc:rut:rutres:200321

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Related research
Keywords: block bootstrap; diffusion processes; multifactor model ; parameter estimation error; specification test; stochastic volatility;

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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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.:
  1. Inoue, Atsushi & Shintani, Mototsugu, 2006. "Bootstrapping GMM estimators for time series," Journal of Econometrics, Elsevier, vol. 133(2), pages 531-555, August. [Downloadable!] (restricted)
    Other versions:
  2. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38. [Downloadable!] (restricted)
  3. Xiaohong Chen & Lars Peter Hansen & Jos´e A. Scheinkman, 2005. "Principal Components and the Long Run," Levine's Bibliography 122247000000000997, UCLA Department of Economics. [Downloadable!]
    Other versions:
  4. 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. [Downloadable!] (restricted)
  5. Valentina Corradi & Norman R. Swanson, 2003. "Evaluation of Dynamic Stochastic General Equilibrium Models Based on Distributional Comparison of Simulated and Historical Data," Departmental Working Papers 200320, Rutgers University, Department of Economics. [Downloadable!]
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  6. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June. [Downloadable!] (restricted)
  7. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March. [Downloadable!] (restricted)
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  8. Donald W. K. Andrews & Moshe Buchinsky, 2000. "A Three-Step Method for Choosing the Number of Bootstrap Repetitions," Econometrica, Econometric Society, vol. 68(1), pages 23-52, January.
  9. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October. [Downloadable!]
  10. 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. [Downloadable!] (restricted)
  11. Nour Meddahi, 2001. "An Eigenfunction Approach for Volatility Modeling," CIRANO Working Papers 2001s-70, CIRANO. [Downloadable!]
  12. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
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  14. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
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  15. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July. [Downloadable!] (restricted)
  16. Donald W.K. Andrews, 1992. "An Introduction to Econometric Applications of Functional Limit Theory for Dependent Random Variables," Cowles Foundation Discussion Papers 1020, Cowles Foundation, Yale University. [Downloadable!]
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  18. Alastair R. Hall & Atsushi Inoue, 2005. "The Large Sample Behaviour of the Generalized Method of Moments Estimator in Misspecified Models," Econometrics 0505002, EconWPA. [Downloadable!]
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  19. Inoue, Atsushi, 2001. "Testing For Distributional Change In Time Series," Econometric Theory, Cambridge University Press, vol. 17(01), pages 156-187, February. [Downloadable!]
  20. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
  21. Sílvia Gonçalves & Halbert White, 2002. "Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models," CIRANO Working Papers 2002s-41, CIRANO. [Downloadable!]
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  22. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  23. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January. [Downloadable!] (restricted)
  24. MEDDAHI, Nour, 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
  25. Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 10(3), pages 525-77.
  26. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(2), pages 385-426. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. Federico M. Bandi & Peter C.B. Phillips, 2005. "A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions," Cowles Foundation Discussion Papers 1522, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  2. Bontemps, Christian & Meddahi, Nour, 2007. "Testing Distributional Assumptions: A GMM Approach," IDEI Working Papers 486, Institut d'Économie Industrielle (IDEI), Toulouse. [Downloadable!]
  3. Valentina Corradi & Norman Swanson & Geetesh Bhardwaj, 2006. "A Simulation Based Specification Test for Diffusion Processes," Departmental Working Papers 200614, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
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