Distribution-free specification test for volatility function based on high-frequency data with microstructure noise

Yinfen Tang, Tao Su and Zhiyuan Zhang ()
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Yinfen Tang: Shanghai Lixin University of Accounting and Finance
Tao Su: Shanghai University of Finance and Economics
Zhiyuan Zhang: Shanghai University of Finance and Economics

Metrika: International Journal for Theoretical and Applied Statistics, 2022, vol. 85, issue 8, No 3, 977-1022

Abstract: Abstract In this paper, we propose a two-step test for parametric specification of volatility function based on high-frequency data with microstructure noise. The latent prices are first recovered at high precision under the assumption that the noise is a parametric function of observable trading information. An asymptotically distribution-free test is then built on the estimated latent prices using Khmaladze martingale transformation. We establish asymptotic theory associated with the test under both the null and alternative hypotheses. Moreover, an extension of the proposed method to incorporate intraday pattern is also formally discussed. Simulation results corroborate our theoretical findings demonstrating clear advantage of our method over an existing distribution-free method that does not take microstructure noise into account. We finally apply the test to the high-frequency data of Standard & Poor’s depository receipt (SPDR) that tracks the S&P 500 index.

Keywords: Diffusion processes; Volatility function; Specification test; High-frequency data; Microstructure noise (search for similar items in EconPapers)
JEL-codes: C14 C22 C32 G12 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00184-021-00857-8

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