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Test for parameter change in diffusion processes by CUSUM statistics based on one-step estimators. (English) Zbl 1095.62100

Summary: We consider the problem of testing for a parameter change using the CUSUM test based on one-step estimators in diffusion processes. It is shown that under regularity conditions the CUSUM test statistic has the limiting distribution of a functional of Brownian bridge.

MSC:

62M02 Markov processes: hypothesis testing
60F05 Central limit and other weak theorems
62M05 Markov processes: estimation; hidden Markov models
62E20 Asymptotic distribution theory in statistics
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