The law of the iterated logarithm for LNQD sequences

Abstract

Abstract Let { ξ i , i ∈ Z } $\{\xi_{i},i\in{\mathbb{Z}}\}$ be a stationary LNQD sequence of random variables with zero means and finite variance. In this paper, by the Kolmogorov type maximal inequality and Stein’s method, we establish the result of the law of the iterated logarithm for LNQD sequence with less restriction of moment conditions. We also prove the law of the iterated logarithm for a linear process generated by an LNQD sequence with the coefficients satisfying ∑ i = − ∞ ∞ | a i | < ∞ $\sum_{i=-\infty}^{\infty}|a_{i}|<\infty$ by a Beveridge and Nelson decomposition.

Keywords

• law of the iterated logarithm
• linear process
• Stein’s method
• LNQD sequence
• Beveridge and Nelson decomposition