UNIFORM ASYMPTOTIC NORMALITY OF WEIGHTED SUMS OF SHORT-MEMORY LINEAR PROCESSES

Let X₁, X₂, … be a short-memory linear process of random variables. For 1 ≤ q < 2, let F be a bounded set of real-valued functions on [0, 1] with finite q-variation. It is proved that { n − 1 / 2 ∑ i = 1 n X i f ( i / n ) : f ∈ F } converges in outer distribution in the Banach space of bounded functions on F as n → ∞. Several applications to a regression model and a multiple change point model are given.