An invariance principle for triangular arrays of dependent variables with application to autocovariance estimation

The invariance principle for triangular arrays of dependent variables is studied. We use the concept of mixingale, proposed by McLeish (1975). Uniform bounds are imposed on the growth of conditional expectations with respect to distant predecessors. The theorem is applied to invariance principles for autocovariance estimates based on triangular arrays of time-series data for weak mixing sequences and linear processes. Such results are required for bootstrap applications.