THE VARIANCE OF AN INTEGRATED PROCESS NEED NOT DIVERGE TO INFINITY, AND RELATED RESULTS ON PARTIAL SUMS OF STATIONARY PROCESSES
Hannes Leeb, Benedikt M. Pötscher · Econometric Theory · 2001
For a process with stationary first differences a necessary and sufficient condition for the variance of the process to be unbounded is given. An example shows that the variance of an integrated process—although unbounded—need not diverge to infinity. Sufficient conditions for the variance of an integrated process to diverge to infinity are provided.