The Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes: The Asymptotically Degenerate Case (Now published in Economic Theory 9 (1993), pp.402-412.)
Published 1992
The central limit theorem in Davidson (1992a) is extended to allow cases where the variances of sequence coordinates can be tending to zero. A trade off is demonstrated between the degree of dependence (mixing size) and the rate of degeneration. For the martingale difference case, it is sufficient for a sum of the variances to diverge at the rate of log n.