Abstract
This paper discusses the problem of testing the equality of two nonparametric regression functions against two-sided alternatives in the presence of long memory in the common covariate and errors. The proposed test is based on a marked empirical process of the differences between the response variables. We discuss asymptotic null distribution of this process and consistency of the test for a class of general alternatives. We also conduct a Monte Carlo simulation study to evaluate the finite sample level and power behavior of the test at some alternatives.
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