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

2009/03/26 by Sergueï Dachian, Serguei Dachian, Dachian, Serguei +2 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability and Risk Models #Statistics Theory (math.ST) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.0903.4642

22 pages, 2 figures

arxiv created 2009/03/26 · openalex publication_date 2009/03/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 α 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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