The Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes: The Asymptotically Degenerate Case

The central limit theorem in Davidson [2] 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 and the rate of degeneration. For the martingale difference case, it is sufficient for the sum of the variances to diverge at the rate of log n.