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A Simulation Based Specification Test for Diffusion Processes

Author

Listed:
  • Valentina Corradi

    () (Queen Mary, University of London)

  • Norman Swanson

    () (Rutgers University)

  • Geetesh Bhardwaj

    () (Rutgerst University)

Abstract

This paper makes two contributions. First, we outline a simple simulation based framework for constructing conditional distributions for multi-factor and multi-dimensional diffusion processes, for the case where the functional form of the conditional density is unknown. The distributions can be used, for example, to form conditional confidence intervals for time period t + ¥ó , say, given information up to period t. Second, we use the simulation based approach to construct a test for the correct specification of a diffusion process. The suggested test is in the spirit of the conditional Kolmogorov test of Andrews (1997). However, in the present context the null conditional distribution is unknown and is replaced by its simulated counterpart. The limiting distribution of the test statistic is not nuisance parameter free. In light of this, asymptotically valid critical values are obtained via appropriate use of the block bootstrap. The suggested test has power against a larger class of alternatives than tests that are constructed using marginal distributions/densities, such as those in A¡§©¥t-Sahalia (1996) and Corradi and Swanson (2005). The findings of a small Monte Carlo experiment underscore the good finite sample properties of the proposed test, and an empirical illustration underscores the ease with which the proposed simulation and testing methodology can be applied.

Suggested Citation

  • Valentina Corradi & Norman Swanson & Geetesh Bhardwaj, 2006. "A Simulation Based Specification Test for Diffusion Processes," Departmental Working Papers 200614, Rutgers University, Department of Economics.
  • Handle: RePEc:rut:rutres:200614
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    References listed on IDEAS

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    Citations

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    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. Chen, Bin & Hong, Yongmiao, 2011. "Generalized spectral testing for multivariate continuous-time models," Journal of Econometrics, Elsevier, vol. 164(2), pages 268-293, October.
    3. Jaeho Yun & Yongmiao Hong, 2013. "A Simulation Test for Continuous-Time Models," WISE Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    4. Papanicolaou, Alex & Giesecke, Kay, 2016. "Variation-based tests for volatility misspecification," Journal of Econometrics, Elsevier, vol. 191(1), pages 217-230.
    5. Bin Chen & Yongmiao Hong, 2013. "Characteristic Function-Based Testing for Multifactor Continuous-Time Markov Models via Nonparametri," WISE Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    6. Kristensen, Dennis, 2011. "Semi-nonparametric estimation and misspecification testing of diffusion models," Journal of Econometrics, Elsevier, vol. 164(2), pages 382-403, October.
    7. Chen, Bin & Hong, Yongmiao, 2014. "A unified approach to validating univariate and multivariate conditional distribution models in time series," Journal of Econometrics, Elsevier, vol. 178(P1), pages 22-44.
    8. Diep Duong & Norman Swanson, 2013. "Density and Conditional Distribution Based Specification Analysis," Departmental Working Papers 201312, Rutgers University, Department of Economics.
    9. repec:hal:journl:peer-00796745 is not listed on IDEAS
    10. repec:wyi:journl:002142 is not listed on IDEAS
    11. 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.
    12. 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.
    13. Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, vol. 173(1), pages 83-107.
    14. 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.
    15. Norman Swanson & Oleg Korenok, 2006. "The Incremental Predictive Information Associated with Using Theoretical New Keynesian DSGE Models Versus Simple Linear Alternatives," Departmental Working Papers 200615, Rutgers University, Department of Economics.
    16. Bin Chen & Yongmiao Hong, 2013. "A Unified Approach to Validating Univariate and Multivariate Conditional Distribution Models in Time Series," WISE Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.

    More about this item

    Keywords

    block bootstrap; diffusion processes; parameter estimation error; simulated GMM; stochastic volatility;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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