The Spurious Regression of Fractionally Integrated Processes With Change Points

Abstract

This paper considers the situation where two independent fractionally integrated processes in presence of change points are used in a linear spurious regression model. By using ordinary least squares regression, the order in probability of t -ratio is derived and its asymptotic distribution is not invariant to shifts in level. Simulation results indicate that, the extent of spurious regression not only seriously depends on the fractionally integrated indexes and sample size, but also is sensitive to the relative location of change points with the sample.