On the Goodness-of-Fit Tests for Some Continuous Time Processes

Details On the Goodness-of-Fit Tests for Some Continuous Time Processes On the Goodness-of-Fit Tests for Some Continuous Time Processes

2009-03-26

arxiv.org/abs/0903.4642v1

Mathematics

Statistics Theory

22 pages, 2 figures

Scientific paper

We present a review of several results concerning the construction of the Cramer-von Mises and Kolmogorov-Smirnov type goodness-of-fit tests for continuous time processes. As the models we take a stochastic differential equation with small noise, ergodic diffusion process, Poisson process and self-exciting point processes. For every model we propose the tests which provide the asymptotic size $\alpha $ and discuss the behaviour of the power function under local alternatives. The results of numerical simulations of the tests are presented.

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