Hypothesis Testing for Families of Dependent Processes ANDREW B. NOBEL University Of North Carolina, Chapel Hill In its simplest form, hypothesis testing seeks to distinguish between two competing explanations for the observed behavior of some phenomena. In this talk, we consider the problem of empirically distinguishing between two known families of dependent processes.  Of particular interest are cases where one or both of the families contains processes exhibiting long range dependence. Sufficient conditions for the discernibility of two (or more) families will be given, and some connections between hypothesis testing and limits to statistical inference will be discussed.  An application of hypothesis testing to the estimation of mixing rates will also be described.