I discuss distributions and moments of ratio statistics associated with quadratic functionals of the ordinary Brownian motion (Bm) and fractional Bm. As far as the ordinary Bm is concerned, quadratic functionals were earlier suggested by several authors as test statistics for goodness of fit tests. Recently, ratios of such functionals were used in time-series based econometrics. In this talk I demonstrate how to derive and compute the distributions of such functionals by using various examples. Moreover I discuss quadratic functionals of the fractional Bm, but it turns out that the case of the fractional Bm is difficult and there remain some problems to be solved. |