The Functional Central Limit Theorem: An Introductory Exposition with Application to Testing for Unit Roots in Economic Time Series

An introductory account of the functional CLT is given which assumes minimal prior knowledge of rigorous probability theory. Both Billingsley's and Pollard's approaches to convergence of stochastic processes are outlined in some detail, and the discussion is illustrated with numerous examples. Proofs, either full or sketches, are included when this aids understanding. Application of the CLT to unit root problems in time series is illustrated by some results from a recent paper by Phillips