The Exponentially Weighted Moving Average (EWMA) is a quantitative or statistical measure used to model or describe a time series. The EWMA is widely used in ...ExponentiallyWeightedMovingAverage(EWMA)AquantitativeorstatisticalmeasureusedtomodelordescribeatimeseriesHome›Resources›Knowledge›Trading&Investing›ExponentiallyWeightedMovingAverage(EWMA)WhatistheExponentiallyWeightedMovingAverage(EWMA)?TheExponentiallyWeightedMovingAverage(EWMA)isaquantitativeorstatisticalmeasureusedtomodelordescribeatimeseries.TheEWMAiswidelyusedinfinance,themainapplicationsbeingtechnicalanalysisandvolatilitymodeling.Themovingaverageisdesignedassuchthatolderobservationsaregivenlowerweights.Theweightsfallexponentiallyasthedatapointgetsolder–hencethenameexponentiallyweighted.TheonlydecisionauseroftheEWMAmustmakeistheparameteralphaAlphaAlphaisameasureoftheperformanceofaninvestmentrelativetoasuitablebenchmarkindexsuchastheS&P500.Analphaofone(thebaselinevalueiszero)showsthatthereturnontheinvestmentduringaspecifiedtimeframeoutperformedtheoverallmarketaverageby1%..TheparameterdecideshowimportantthecurrentobservationisinthecalculationoftheEWMA.Thehigherthevalueofalpha,themorecloselytheEWMAtrackstheoriginaltimeseries. EWMAFormulaTheEWMA’ssimplemathematicalformulationdescribedbelow:  Where:Alpha=Theweightdecidedbytheuserr=Valueoftheseriesinthecurrentperiod TheEWMAisarecursivefunction,whichmeansthatthecurrentobservationiscalculatedusingthepreviousobservation.TheEWMA’srecursivepropertyleadstotheexponentiallydecayingweightsasshownbelow:  Theaboveequationcanberewrittenintermsofolderweights,asshownbelow:  Itcanbefurtherexpandedbygoingbackanotherperiod:  TheprocesscontinuesuntilwereachthebasetermEWMA0.TheequationcanberearrangedtoshowthattheEWMAtistheweightedaverageofalltheprecedingobservations,wheretheweightoftheobservationrt–kisgivenby:  Sincealphaisbetween0and1,theweightbecomessmalleraskbecomeslarger.Inotherwords,aswegobackfurtherinhistory,theweightbecomessmaller.Thefactisillustratedinthechartbelow,whi