Long memory measures – fractional integration parameter, Hurst exponent

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1、TimeSeriesAnalysisandForecastingClasses13:Longmemorymeasures–fractionalintegrationparameter,HurstexponentContents:1.Longmemoryofaseries...........................................................................................................1Example13.1:Randomwalkprocess..........................

2、.....................................................2Example13.2:AstationaryAR(1)process.......................................................................22.TheperiodogramforlnSP500,computedingretl........................................................................63.Periodogramcomputedi

3、ngretl,forlogreturnsoftheindex......................................................74.Exampleformacroeconomicmonthlydata.................................................................................9Example13.3:Periodogramforunemploymentrate.....................................................

4、.....13Example13.4:Differencesofunemploymentrate.............................................................16Exercises...........................................................................................................................................17Referencesandadditionalreading:......

5、.............................................................................................201.LongmemoryofaseriesLongmemoryisshownbysignificantcorrelationcoefficientsofaserieswithitslaggedvalues,evenforlargenumberoflags.ItcanbecheckedvisuallywithuseofACFandPACFgraphs,canbetestedwithuseofcorrela

6、tioncoefficientsignificancetests,ortheLjung-BoxandBox-Piercetests.Therearesomeothermethodsofdetectingshortandlongmemoryintheseries,andtoclassifybehaviorofaseries:fractionalintegrationparameter,theHurstexponent,andtheLomodifiedrescaledrangestatistic.Severalmethodsoffractionalintegrationparameterest

7、imationarebasedontechniquesofspectralanalysis.1Spectralanalysishasmanyapplications:-assimpletoolusedtocheckseasonalityand/orcyclicalbehaviorofaneconomicvariable;-„technicalapplication”–wholeenergycanbeexpressedas