Let Xn = ∞j =−∞ aj εn−j, n 1, be a non-causal linear process with weights aj ’s satisfying certain summability conditions, and the iid sequence of innovation {εi } having zero mean and finite second moment. For a large class of non-linear functional K which includes indicator functions and polynomials, the present paper develops the √N central limit theorem for the partial sums SN = N n=1 [K(Xn)−EK(Xn)] .
關聯:
Journal of Theoretical Probability, 18(2): 345-358