Empirical $$L^2$$ L 2 -distance test statistics for ergodic diffusions

A. Gregorio () and Stefano Iacus ()
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A. Gregorio: “Sapienza” University of Rome

Statistical Inference for Stochastic Processes, 2019, vol. 22, issue 2, No 3, 233-261

Abstract: Abstract The aim of this paper is to introduce a new type of test statistic for simple null hypothesis on one-dimensional ergodic diffusion processes sampled at discrete times. We deal with a quasi-likelihood approach for stochastic differential equations (i.e. local gaussian approximation of the transition functions) and define a test statistic by means of the empirical $$L^2$$ L 2 -distance between quasi-likelihoods. We prove that the introduced test statistic is asymptotically distribution free; namely it weakly converges to a $$\chi ^2$$ χ 2 random variable. Furthermore, we study the power under local alternatives of the parametric test. We show by the Monte Carlo analysis that, in the small sample case, the introduced test seems to perform better than other tests proposed in literature.

Keywords: Asymptotic distribution free test; Local alternatives; Maximum-likelihood type estimator; Discrete observations; Quasi-likelihood function; Stochastic differential equation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11203-018-9176-x

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