Central limit theorems for linear, nonlinear and mixing processes

摘要

In the past, several mixing conditions have been proposed to characterize the modes of dependence for stationary stochastic processes and various laws of weak and strong convergence have been investigated for processes satisfying these mixing properties. On the other hand, time series analysts have suggested several structures of dependence which, for instance, describe the linear, bilinear, Volterra and other nonlinear systems and they have explored the large sample properties of various statistics derived from samples drawn of these processes. An attempt will be made in this article to compare these two approaches (with special reference to the classical Central Limit Theorem and its extensions) and establish some common ground between them.