Divergences test statistics for discretely observed diffusion processes

Abstract: In this paper we propose the use of as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process , from discrete observations with , , under the asymptotic scheme , and . The class of is wide and includes several special members like Kullback–Leibler, Rényi, power and . We derive the asymptotic distribution of the test statistics based on the estimated . The asymptotic distribution depends on the regularity of the function and in general it differs from the standard distribution as in the i.i.d. case. Numerical analysis is used to show the small sample properties of the test statistics in terms of estimated level and power of the test. [Copyright &y& Elsevier]