Spurious Regressions of Stationary AR(p) Processes with Structural Breaks

When a pair of independent series are highly persistent, there is a spurious regression bias in a regression between these series, closely related to the classic studies of Granger and Newbold [1974]. Although this is well known to occur with independent I(1) processes, this paper provides theoretical and numerical evidences that the phenomenon of spurious regression also arises in regressions between stationary AR(p) processes with structural breaks in the means and the trends. An intuition behind this is that structural breaks can increase the persistence levels in the processes (see, e.g., Granger and Hyung [2004]), which then leads to spurious regressions. These phenomena occur for general distributions and serial dependence of the innovation terms