We consider statistical inference in the presence of serial dependence. The main focus is on use of statistics that are constructed as if no dependence were believed present, and are asymptotically normal in the presence of dependence. Typically the variance in the limit distribution is affected by the dependence, and needs to be consistently estimated. We discuss first the leading caes of location and regression models, stressing least squares estimation. We then consider the use of robust estimates, such as M-estimates, in these models. We go on to discuss more general statistical models, including econometric models. The rules of inference adopted in these cases typically involve use of a bandwidth or smoothing number when the dependence introduces a nonparametric aspect, and we discuss choice of such numbers. We then consider some possibilities for improved inference by use of higher-order asymptotic theory and the bootstrap. The dependence considered in the paper is mostly of short-range type, but we also discuss forms of long-range dependence. Finally, we consider inference based on smoothed nonparametric estimates of probability densities and regression functions, where dependence often has no effect on first-order asymptotics.
