An exponential moving average (EMA), also known as an exponentially weighted moving average (EWMA), is a first-order infinite impulse response filter that ...MovingaverageFromWikipedia,thefreeencyclopediaJumptonavigationJumptosearchForthestatisticalprocess,seeMovingaveragemodel.Forotheruses,seeMovingaverage(disambiguation).typeofstatisticalmeasureoversubsetsofadatasetAnexampleoftwomovingaveragecurvesInstatistics,amovingaverage(rollingaverageorrunningaverage)isacalculationtoanalyzedatapointsbycreatingaseriesofaveragesofdifferentsubsetsofthefulldataset.Itisalsocalledamovingmean(MM)[1]orrollingmeanandisatypeoffiniteimpulseresponsefilter.Variationsinclude:simple,cumulative,orweightedforms(describedbelow).Givenaseriesofnumbersandafixedsubsetsize,thefirstelementofthemovingaverageisobtainedbytakingtheaverageoftheinitialfixedsubsetofthenumberseries.Thenthesubsetismodifiedby"shiftingforward";thatis,excludingthefirstnumberoftheseriesandincludingthenextvalueinthesubset.Amovingaverageiscommonlyusedwithtimeseriesdatatosmoothoutshort-termfluctuationsandhighlightlonger-termtrendsorcycles.Thethresholdbetweenshort-termandlong-termdependsontheapplication,andtheparametersofthemovingaveragewillbesetaccordingly.Forexample,itisoftenusedintechnicalanalysisoffinancialdata,likestockprices,returnsortradingvolumes.Itisalsousedineconomicstoexaminegrossdomesticproduct,employmentorothermacroeconomictimeseries.Mathematically,amovingaverageisatypeofconvolutionandsoitcanbeviewedasanexampleofalow-passfilterusedinsignalprocessing.Whenusedwithnon-timeseriesdata,amovingaveragefiltershigherfrequencycomponentswithoutanyspecificconnectiontotime,althoughtypicallysomekindoforderingisimplied.Viewedsimplisticallyitcanberegardedassmoothingthedata.Contents1Simplemovingaverage2Cumulativemovingaverage3Weightedmovingaverage4Exponentialmovingaverage4.1ApproximatingtheEMAwithalimitednumberofterms4.2RelationshipbetweenSMAandEMA4.3Exponentiallyweightedmovingvarianceandstandarddeviation4.4Modifiedmovingaverage4.5Applic