Statistica Sinica 3(1993), 453-480

MOMENT BOUNDS FOR DERIVING TIME SERIES CLT'S

AND MODEL SELECTION PROCEDURES

David F. Findley and Ching-Zong Wei

Bureau of the Census and Academia Sinica

Abstract: We establish a 2pth moment bound (p>=1) for quadratic forms, and a pth moment bound for an important ratio of such forms, for vector time series having estimated regression mean functions and stationary, square summable autocovariances. The mean-centered series are assumed to have a joint linear representation in terms of a martingale difference sequence with bounded conditional 4pth moments. Applications discussed include a quite general Central Limit Theorem for sample covariances and the derivation of several model selection methods for stochastic regression, among them methods concerned with multi-step-ahead forecasting performance.

Key words and phrases: Sample covariances, stationary regressor selection, Vuong's test, multi-step-ahead forecast-model comparisons, quadratic forms, nonstationary