Open Access
December, 1987 Testing That a Stationary Time Series is Gaussian
T. W. Epps
Ann. Statist. 15(4): 1683-1698 (December, 1987). DOI: 10.1214/aos/1176350618


A class of procedures is proposed for testing the composite hypothesis that a stationary stochastic process is Gaussian. Requiring very limited prior knowledge about the structure of the process, the tests rely on quadratic forms in deviations of certain sample statistics from their population counterparts, minimized with respect to the unknown parameters. A specific test is developed, which employs differences between components of the sample and Gaussian characteristic functions, evaluated at certain points on the real line. By demonstrating that, under $H_0$, the normalized empirical characteristic function converges weakly to a continuous Gaussian process, it is shown that the test remains valid when arguments of the characteristic functions are in certain ways data dependent.


Download Citation

T. W. Epps. "Testing That a Stationary Time Series is Gaussian." Ann. Statist. 15 (4) 1683 - 1698, December, 1987.


Published: December, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0644.62093
MathSciNet: MR913582
Digital Object Identifier: 10.1214/aos/1176350618

Primary: 62M10
Secondary: 60G15

Keywords: Chi-squared test , Empirical characteristic function , Gaussian process , Goodness-of-fit test , normal distribution , Spectral density , stochastic process , weak convergence

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 4 • December, 1987
Back to Top