On a family of test statistics for discretely observed diffusion processes
AbstractWe consider parametric hypotheses testing for multidimensional ergodic diffusion processes observed at discrete time. We propose a family of test statistics, related to the so called phi-divergence measures. By taking into account the quasi-likelihood approach developed for studying the stochastic differential equations, it is proved that the tests in this family are all asymptotically distribution free. In other words, our test statistics weakly converge to the chi squared distribution. Furthermore, our test statistic is compared with the quasi likelihood ratio test. In the case of contiguous alternatives, it is also possible to study in detail the power function of the tests. Although all the tests in this family are asymptotically equivalent, we show by Monte Carlo analysis that, in the small sample case, the performance of the test strictly depends on the choice of the function phi. Furthermore, in this framework, the simulations show that there are not uniformly most powerful tests.
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Bibliographic InfoPaper provided by Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano in its series Departmental Working Papers with number 2011-37.
Date of creation: 17 Dec 2011
Date of revision:
Discrete observations; distribution free tests; generalized likelihood ratio tests; parametric hypotheses testing; quasi-likelihood functions; stochastic differential equations;
Other versions of this item:
- Alessandro De Gregorio & Stefano Iacus, 2011. "On a family of test statistics for discretely observed diffusion processes," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1114, Universitá degli Studi di Milano.
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