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Characteristic Function–Based Testing For Multifactor Continuous-Time Markov Models Via Nonparametric Regression

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  • Chen, Bin
  • Hong, Yongmiao

Abstract

We develop a nonparametric regression-based goodness-of-fit test for multifactor continuous-time Markov models using the conditional characteristic function, which often has a convenient closed form or can be approximated accurately for many popular continuous-time Markov models in economics and finance. An omnibus test fully utilizes the information in the joint conditional distribution of the underlying processes and hence has power against a vast class of continuous-time alternatives in the multifactor framework. A class of easy-to-interpret diagnostic procedures is also proposed to gauge possible sources of model misspecification. All the proposed test statistics have a convenient asymptotic N (0, 1) distribution under correct model specification, and all asymptotic results allow for some data-dependent bandwidth. Simulations show that in finite samples, our tests have reasonable size, thanks to the dimension reduction in nonparametric regression, and good power against a variety of alternatives, including misspecifications in the joint dynamics, but the dynamics of each individual component is correctly specified. This feature is not attainable by some existing tests. A parametric bootstrap improves the finite-sample performance of proposed tests but with a higher computational cost.

Suggested Citation

  • Chen, Bin & Hong, Yongmiao, 2010. "Characteristic Function–Based Testing For Multifactor Continuous-Time Markov Models Via Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 26(04), pages 1115-1179, August.
  • Handle: RePEc:cup:etheor:v:26:y:2010:i:04:p:1115-1179_99
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    Cited by:

    1. 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.
    2. Breunig, Christoph & Hoderlein, Stefan, 2018. "Specification Testing in Random Coefficient Models," Rationality and Competition Discussion Paper Series 77, CRC TRR 190 Rationality and Competition.
    3. 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.
    4. 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.
    5. Polanski, Arnold & Stoja, Evarist, 2012. "Efficient evaluation of multidimensional time-varying density forecasts, with applications to risk management," International Journal of Forecasting, Elsevier, vol. 28(2), pages 343-352.
    6. Nadarajah, Saralees & Chan, Stephen & Afuecheta, Emmanuel, 2013. "On the characteristic function for asymmetric Student t distributions," Economics Letters, Elsevier, vol. 121(2), pages 271-274.
    7. 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.

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