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Econometrics Paper
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.)
James Davidson  1992
Paper No' EM/1992/243:

Tags: central limit theorem; sequence coordinates; rate of degeneration; mixing processes; martingale difference.

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.