 Non-asymptotic statistical tests of the diffusion coefficient of stochastic differential equationsAnna Melnykova, Patricia Reynaud-Bouret and Adeline Samson Stochastic Processes and their Applications, 2024, vol. 173, issue C Abstract: We develop several statistical tests of the determinant of the diffusion coefficient of a stochastic differential equation, based on discrete observations on a time interval [0,T] sampled with a time step Δ. Our main contribution is to control the test Type I and Type II errors in a non asymptotic setting, i.e. when the number of observations and the time step are fixed. The test statistics are calculated from the process increments. In dimension 1, the density of the test statistic is explicit. In dimension 2, the test statistic has no explicit density but upper and lower bounds are proved. We also propose a multiple testing procedure in dimension greater than 2. Every test is proved to be of a given non-asymptotic level and separability conditions to control their power are also provided. A numerical study illustrates the properties of the tests for stochastic processes with known or estimated drifts. Keywords: Statistical tests; Non-asymptotic settings; Stochastic Differential Equation; Diffusion coefficient (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:173:y:2024:i:c:s0304414924000784 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2024.104372 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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