Testing of nonstationarities in the unit circle, long memory processes and the day of the week effects in financial data

This paper examines a version of the tests of Robinson (1994) that enables one to test models of the form (1-Lk)dxt = ut, where k is an integer value, d may be any real number, and ut is I(0). The most common cases are those with k = 1 (unit or fractional roots) and k = 4 and 12 (seasonal unit or fractional models). However, we extend the analysis to cover situations such as (1-L5)d xt = ut, which might be relevant, for example, in the context of financial time series data. We apply these techniques to the daily Eurodollar rate and Dow Jones index, and find that for the former series the most adequate specifications are either a pure random walk or a model of the form xt = xt-5 + εt, implying in both cases that the returns are completely unpredictable. In the case of Dow Jones index, a model of the form (1-L5)d xt = ut is selected, with d constrained between 0.50 and 1, implying nonstationarity and mean-reverting behaviour