The spurious regression of fractionally integrated processes

This paper extends the theoretical analysis of the spurious regression and spurious detrending from the usual I(1) processes to the long memory fractionally integrated processes. It is found that when we regress a long memory fractionally integrated process on another unrelated long memory fractionally integrated process, no matter whether these processes are stationary or not, as long as their orders of integration sum up to a value greater than 0.5, the t ratios become divergent and spurious effects occur. Our finding suggests that it is the long memory, instead of nonstationarity or lack of ergodicity, that causes such spurious effects. As a result, spurious effects might happen more often than we previously believed as they can arise even between stationary series while the usual first-differencing procedure may not completely eliminate spurious effects when data possess strong long memory.