Goodness-of-Fit Tests for Ornstein-Uhlenbeck Process

Details Goodness-of-Fit Tests for Ornstein-Uhlenbeck Process Goodness-of-Fit Tests for Ornstein-Uhlenbeck Process

2012-03-16

arxiv.org/abs/1203.3694v1

Mathematics

Statistics Theory

11 pages

Scientific paper

We consider the goodness of fit testing problem for linear stochastic differential equation (Ornstein-Uhlenbeck process). The basic hypothesis is supposed to be composite with two-dimensional unknown parameter. We study two goodness of fit tests of Cramer-von Mises type based on empirical distribution function and on local time estimator of the invariant density. It is shown that the limit distributions of the underlying statistics under hypothesis do not depend on the unknown parameter.

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