Time-Invariant Restrictions of Volatility Functionals: Efficient Estimation and Specification Tests

70 Pages Posted: 20 Jan 2019 Last revised: 14 Oct 2019

See all articles by Xiye Yang

Xiye Yang

Rutgers, The State University of New Jersey - Department of Economics

Date Written: October 11, 2019

Abstract

This paper studies the estimation and inference problems for time-invariant restrictions on certain functions of the stochastic volatility process. We first develop a more efficient GMM estimator and derive the efficiency bound under such restrictions. Then we construct an integrated Hausman-type test by summing up the standardized squared differences between this more efficient estimator and the unrestricted estimator, which is less efficient under the null but consistent under both the null and the alternative, at different time points. This efficient GMM estimator can also be used to update an existing Bierens-type test and simplifies the calculation of the asymptotic variance. Since quadratic function puts more weights on large values, the Hausman-type test can have superior power than the Bierens-type test, which is based on a linear function of the differences. Simulation study shows that except for very small local window size, the Hausman-type test has good size and superior power. We finally apply these tests to studying the constant beta hypothesis using empirical data and find substantial evidence against this hypothesis.

Keywords: Specification test, volatility functionals, efficiency, high frequency data

JEL Classification: C12, C58

Suggested Citation

Yang, Xiye, Time-Invariant Restrictions of Volatility Functionals: Efficient Estimation and Specification Tests (October 11, 2019). Available at SSRN: https://ssrn.com/abstract=3319483 or http://dx.doi.org/10.2139/ssrn.3319483

Xiye Yang (Contact Author)

Rutgers, The State University of New Jersey - Department of Economics ( email )

75 Hamilton Street
New Brunswick, NJ 08901
United States

HOME PAGE: http://economics.rutgers.edu/people/474-xiye-yang

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