Probabilities of Moderate Devla Tions for Non-Stationary m-Dependent Processes with Unbounded m

Abstract

For each [Formula: see text] be an m-dependent sequence of (possibly non-stationary) random variables, where [Formula: see text] It is assumed that [Formula: see text] exists and is non-zero. Under the above and other assumptions, it is proved that for every c > 0, [Formula: see text] and [Formula: see text] as [Formula: see text] The above probabilities of moderate deviations results generalize similar findings of Ghosh (1974) for stationary m-dependent sequences with fixed m.