Title: Regressions with fractional d=0.5 and weakly nonstationary processes
Authors: Ioannis Kasparis - University of Cyprus (Cyprus) [presenting]
James Duffy - Oxford (United Kingdom)
Abstract: Despite major advances in the statistical analysis of fractionally integrated time series models, no limit theory is available for sample averages of fractionally integrated processes with memory parameter d=0.5. We provide limit theory for sample averages of a general class of nonlinear transformations of fractional d=0.5 (I(0.5)) and Mildly Integrated (MI) processes. Although I(0.5) processes lie in the nonstationary region, the asymptotic machinery that is routinely used for I(d), d>1/2 is not valid in the I(0.5) case. In particular, FCLTs are not applicable to I(0.5) processes and a different approach is required. A general method that applies to both I(0.5) and MI processes is proposed. We show that sample averages of transformations of I(0.5) and MI processes converge in distribution to the convolution of the transformation function and some Gaussian density evaluated at a possibly random point. The type of nonlinear transformations under consideration accommodates a wide range of regression models used in empirical work including step type discontinuous functions, functions with integrable poles as well as integrable kernel functions that involve bandwidth terms. Our basic limit theory is utilised for the asymptotic analysis of the LS and the Nadaraya-Watson kernel regression estimator.