Empirical L^2-distance test statistics for ergodic diffusions
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-distance between quasi-likelihoods. We prove that the introduced test statistic is asymp- totically distribution free; namely it weakly converges to a chi squared random variable.