Influence Functionals for Time Series

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. A definition is given for influence functionals of parameter estimates in time-series models. The definition involves the use of a contaminated observations process of the form yty = (1 -zJy)xt + zy wt, t = 1,2,.. 0 < y < 1, where xt is a core process (usually Gaussian), wt is a contaminat-ing process, and zy is a zero-one process with P (zy = 1) = y + o(y). This form is sufficiently general to model such diverse contamination types as isolated outliers and patches of outliers. Let T(y) denote the functional representation of a given estimate, where the measures ,y 0 < y < 1 for yty are in an appropriate subset of the family of stationary and ergodic measures