ON NON-UNIFORM BERRY–ESSEEN BOUNDS FOR TIME SERIES
Abstract: Given a stationary sequence , non-uniform bounds for the normal
approximation in the Kolmogorov metric are established. The underlying weak dependence
assumption includes many popular linear and nonlinear time series from the literature, such
as ARMA or GARCH models. Depending on the number of moments , typical
bounds in this context are of the size , where we often find that
. In our setup, we can essentially improve upon this rate by the
factor , yielding a bound of . Among other things,
this allows us to recover a result from the literature, which is due to Ibragimov.
2000 AMS Mathematics Subject Classification: Primary: 60F05; Secondary:
91B84.
Keywords and phrases: Berry–Esseen, weak dependence.