IDEAS home Printed from https://ideas.repec.org/p/rut/rutres/200321.html
   My bibliography  Save this paper

Bootstrap Specification Tests for Diffusion Processes

Author

Listed:
  • Valentina Corradi

    () (Queen Mary, University of London)

  • Norman R. Swanson

    () (Rutgers University)

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.

Suggested Citation

  • Valentina Corradi & Norman R. Swanson, 2003. "Bootstrap Specification Tests for Diffusion Processes," Departmental Working Papers 200321, Rutgers University, Department of Economics.
  • Handle: RePEc:rut:rutres:200321
    as

    Download full text from publisher

    File URL: http://www.sas.rutgers.edu/virtual/snde/wp/2003-21.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Corradi, Valentina & Swanson, Norman R., 2002. "A consistent test for nonlinear out of sample predictive accuracy," Journal of Econometrics, Elsevier, vol. 110(2), pages 353-381, October.
    2. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    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. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    5. Corradi, Valentina & Swanson, Norman R., 2007. "Evaluation of dynamic stochastic general equilibrium models based on distributional comparison of simulated and historical data," Journal of Econometrics, Elsevier, vol. 136(2), pages 699-723, February.
    6. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    7. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-952, July.
    8. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    9. Nour Meddahi, 2001. "An Eigenfunction Approach for Volatility Modeling," CIRANO Working Papers 2001s-70, CIRANO.
    10. Goncalves, Silvia & White, Halbert, 2004. "Maximum likelihood and the bootstrap for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 119(1), pages 199-219, March.
    11. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
    12. Xiaohong Chen & Lars Peter Hansen & Jos´e A. Scheinkman, 2005. "Principal Components and the Long Run," Levine's Bibliography 122247000000000997, UCLA Department of Economics.
    13. Antonio Mele & Filippo Altissimo, 2004. "Simulated Nonparametric Estimation of Continuous Time Models of Asset Prices and Returns," FMG Discussion Papers dp476, Financial Markets Group.
    14. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
    15. Inoue, Atsushi & Shintani, Mototsugu, 2006. "Bootstrapping GMM estimators for time series," Journal of Econometrics, Elsevier, vol. 133(2), pages 531-555, August.
    16. Hall, Alastair R. & Inoue, Atsushi, 2003. "The large sample behaviour of the generalized method of moments estimator in misspecified models," Journal of Econometrics, Elsevier, vol. 114(2), pages 361-394, June.
    17. Yacine Aït-Sahalia, 2001. "Transition Densities For Interest Rate And Other Nonlinear Diffusions," World Scientific Book Chapters,in: Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 1, pages 1-34 World Scientific Publishing Co. Pte. Ltd..
    18. 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.
    19. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
    20. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    21. 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.
    22. Inoue, Atsushi, 2001. "Testing For Distributional Change In Time Series," Econometric Theory, Cambridge University Press, vol. 17(01), pages 156-187, February.
    23. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    24. Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 525-577.
    25. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
    26. 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.
    27. Bühlmann, Peter, 1995. "The blockwise bootstrap for general empirical processes of stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 247-265, August.
    28. 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 for Research in Economics, Yale University.
    29. Radulovic, Dragan, 1996. "The bootstrap for empirical processes based on stationary observations," Stochastic Processes and their Applications, Elsevier, vol. 65(2), pages 259-279, December.
    30. Dai, Qiang & Singleton, Kenneth J., 2002. "Expectation puzzles, time-varying risk premia, and affine models of the term structure," Journal of Financial Economics, Elsevier, vol. 63(3), pages 415-441, March.
    31. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Corradi, Valentina & Swanson, Norman R., 2011. "Predictive density construction and accuracy testing with multiple possibly misspecified diffusion models," Journal of Econometrics, Elsevier, vol. 161(2), pages 304-324, April.
    2. Papanicolaou, Alex & Giesecke, Kay, 2016. "Variation-based tests for volatility misspecification," Journal of Econometrics, Elsevier, vol. 191(1), pages 217-230.
    3. Kristensen, Dennis, 2010. "Pseudo-maximum likelihood estimation in two classes of semiparametric diffusion models," Journal of Econometrics, Elsevier, vol. 156(2), pages 239-259, June.
    4. Kristensen, Dennis, 2011. "Semi-nonparametric estimation and misspecification testing of diffusion models," Journal of Econometrics, Elsevier, vol. 164(2), pages 382-403, October.
    5. Chen, Qiang & Zheng, Xu & Pan, Zhiyuan, 2015. "Asymptotically distribution-free tests for the volatility function of a diffusion," Journal of Econometrics, Elsevier, vol. 184(1), pages 124-144.
    6. Diep Duong & Norman Swanson, 2013. "Density and Conditional Distribution Based Specification Analysis," Departmental Working Papers 201312, Rutgers University, Department of Economics.
    7. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    8. Xiangjin Shen & Hiroki Tsurumi, 2011. "Comparison of Bayesian Model Selection Criteria and Conditional Kolmogorov Test as Applied to Spot Asset Pricing Models," Departmental Working Papers 201126, Rutgers University, Department of Economics.
    9. Cai, Lili & Swanson, Norman R., 2011. "In- and out-of-sample specification analysis of spot rate models: Further evidence for the period 1982-2008," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 743-764, September.
    10. Zu, Yang & Boswijk, H. Peter, 2017. "Consistent nonparametric specification tests for stochastic volatility models based on the return distribution," Journal of Empirical Finance, Elsevier, vol. 41(C), pages 53-75.
    11. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    12. Fuchun Li, 2015. "Testing for the Diffusion Matrix in a Continuous-Time Markov Process Model with Applications to the Term Structure of Interest Rates," Staff Working Papers 15-17, Bank of Canada.
    13. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    14. Bandi, Federico M. & Phillips, Peter C.B., 2007. "A simple approach to the parametric estimation of potentially nonstationary diffusions," Journal of Econometrics, Elsevier, vol. 137(2), pages 354-395, April.
    15. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    16. Gao, Jiti & Casas, Isabel, 2008. "Specification testing in discretized diffusion models: Theory and practice," Journal of Econometrics, Elsevier, vol. 147(1), pages 131-140, November.
    17. Song, Zhaogang, 2011. "A martingale approach for testing diffusion models based on infinitesimal operator," Journal of Econometrics, Elsevier, vol. 162(2), pages 189-212, June.
    18. Bhardwaj, Geetesh & Corradi, Valentina & Swanson, Norman R., 2008. "A Simulation-Based Specification Test for Diffusion Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 176-193, April.
    19. 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.
    20. Aït-Sahalia, Yacine & Park, Joon Y., 2012. "Stationarity-based specification tests for diffusions when the process is nonstationary," Journal of Econometrics, Elsevier, vol. 169(2), pages 279-292.
    21. Li, Gang & Zhang, Chu, 2013. "Diagnosing affine models of options pricing: Evidence from VIX," Journal of Financial Economics, Elsevier, vol. 107(1), pages 199-219.
    22. Diep Duong & Norman R. Swanson, 2011. "Volatility in Discrete and Continuous Time Models: A Survey with New Evidence on Large and Small Jumps," Departmental Working Papers 201117, Rutgers University, Department of Economics.
    23. Zu, Yang, 2015. "Nonparametric specification tests for stochastic volatility models based on volatility density," Journal of Econometrics, Elsevier, vol. 187(1), pages 323-344.

    More about this item

    Keywords

    block bootstrap; diffusion processes; multifactor model ; parameter estimation error; specification test; stochastic volatility;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:rut:rutres:200321. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://edirc.repec.org/data/derutus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.