Maximal Inequalities and an Application Under a Weak Dependence

Abstract

Abstract. We establish maximal moment inequalities of partial sums under ψ-weak dependence, which has been proposed by Doukhan and Louhichi [P. Doukhan and S. Louhichi, A new weak dependence condition and application to moment inequality, Stochastic Process. Appl. 84 (1999), 313-342], to unify weak dependence such as mixing, association, Gaussian sequences and Bernoulli shifts. As an application of maximal moment inequalities, a functional central limit theorem is developed for linear processes with ψ-weakly dependent innovations.

A class of CUSUM tests using empirical distributions for tail changes in weakly dependent processes

“…The ψ-weakly dependent processes, including all classes of weakly dependent stationary processes of interest in statistics under natural conditions on the process parameters have been actively studied by many researchers: Coulon-Prieur and Doukhan (2000) for a central limit theorem under the weak dependence condition, Doukhan and Louhichi (2001) for functional estimation of the density, Ango Nze et al (2002) for nonparametric regression estimation with the weak dependence, Ango Nze and Doukhan (2004) for the weakly dependent time series models and applications to econometrics, Doukhan and Neumann (2007), Hwang and Shin (2013) and Doukhan et al (2015) for probabilistic results of the processes such as moment inequalities and distribution functions. Also see Hwang and Shin (2011, 2012a, 2012b, 2016a, 2016b and references.…”