Testing for Changes in the Mean or Variance of Long Memory Processes

Inthispaper,westudytheasymptoticCUSUMtestsfordetectingchangesinthemeanorvarianceofamoving-averageprocesswithlongmemory.Whenthereisnochangeover[O,T],theasymptoticdistributionoftheteststatisticisderived,whichallowsustofindasymptoticcriticalvalues.Whenthereisachange,thebehavioroftheteststatisticisdiscussed.Conditionsfortheconsistencyofthesetestsarealsodiscussed.Basedontheasymptoticresults,simulationstudiesoftestingforchangesinthemeanshowthattheCUSUMtestproposedperformswell.