Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 3, 357--369

THE MODIFIED CRAMÉR-VON MISES GOODNESS-OF-FIT CRITERION FOR TIME SERIES

By

T. W. ANDERSON, *Stanford University, U. S. A*

And

M. A. STEPHENS, *Simon Fraser University, Canada*

SUMMARY. The general theory of finding the distribution of a quadratic integral of a continuous time Gaussian stochastic process with a given covariance function has been sketched with reference to the Cramer-Von Mises criterion to test for a given probability distribution. The result is employed to provide tests for the *MA*(1) and *AR*(1) processes and the corresponding distributions of test statistics.

*Subject classification*. 62M10