Tail and Non-Tail Memory with Applications to Extreme Value and Robust Statistics, Revised for Econometric Theory, www.unc.edu/jbhill/tail_nontail_garch.pdf

New notions of tail and non-tail dependence are used to characterize sep-arately extremal and non-extremal information, including tail log-exceedances and events, and tail-trimmed levels. We prove Near Epoch Dependence (McLeish 1975, Gallant and White 1988) and L0-Approximability (Pötscher and Prucha 1991) are equivalent for tail events and tail-trimmed levels, ensuring a Gaussian central limit theory for important extreme value and robust statistics under general conditions. We apply the theory to characterize the extremal and non-extremal memory properties of possibly very heavy tailed GARCH processes and distributed lags. This in turn is used to verify Gaussian limits for tail in-dex, tail dependence and tail trimmed sums of these data, allowing for Gaussian asymptotics for a new Tail-Trimmed Least Squares estimator for heavy tailed processes. 1. INTRODUCTION W