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A nonparametric specification test for the volatility functions of diffusion processes

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  • Qiang Chen
  • Meidi Hu
  • Xiaojun Song

Abstract

This paper develops a new test for the parametric volatility function of a diffusion model based on nonparametric estimation techniques. The proposed test imposes no restriction on the functional form of the drift function and has an asymptotically standard normal distribution under the null hypothesis of correct specification. It is consistent against any fixed alternatives and has nontrivial asymptotic power against a class of local alternatives with proper rates. Monte Carlo simulations show that the test performs well in finite samples and generally has better power performance than the nonparametric test of Li (2007) and the stochastic process-based tests of Dette and Podolskij (2008). When applying the test to high frequency data of EUR/USD exchange rate, the empirical results show that the commonly used volatility functions fit more poorly when the data frequency becomes higher, and the general volatility functions fit relatively better than the constant volatility function.

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  • Qiang Chen & Meidi Hu & Xiaojun Song, 2019. "A nonparametric specification test for the volatility functions of diffusion processes," Econometric Reviews, Taylor & Francis Journals, vol. 38(5), pages 557-576, May.
    • Handle: RePEc:taf:emetrv:v:38:y:2019:i:5:p:557-576
    DOI: 10.1080/07474938.2017.1365428
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    Cited by:

    1. Li, Yingying & Liu, Guangying & Zhang, Zhiyuan, 2022. "Volatility of volatility: Estimation and tests based on noisy high frequency data with jumps," Journal of Econometrics, Elsevier, vol. 229(2), pages 422-451.

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