Copulas and time series with long-ranged dependencesCopulas与长程相关时间序列

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1、Copulasandtimeserieswithlong-rangeddependencesRemyChicheporticheandAnirbanChakrabortiyChairedenancequantitative,EcoleCentraleParis,92295Ch^atenay-Malabry,France(Dated:July16,2018)Wereviewideasontemporaldependencesandrecurrencesindiscretetimeseriesfromseveralareasofnaturalandsoci

2、alsciences.Werevisitexistingstudiesandredenetherelevantobserv-ablesinthelanguageofcopulas(jointlawsoftheranks).Weproposethatcopulasprovideanappropriatemathematicalframeworktostudynon-lineartimedependencesandrelatedconcepts

3、likeaftershocks,Omorilaw,recurrences,waitingtimes.Wealsocri

4、ticallyargueusingthisglobalapproachthatpreviousphenomenologicalattemptsinvolvingonlyalong-rangedautocorrelationfunctionlackedcomplexityinthattheywereessentiallymono-scale.PACSnumbers:05.45.Tp,02.50.-r,87.85.NgKeywords:Recurrenceintervals,copulas,long-rangedcorrelations,timeseriesI.I

5、NTRODUCTIONetal.[5]hadsuggestedauniedscalinglawcombiningtheGutenberg-Richterlaw,theOmorilaw,andthefrac-Athoroughunderstandingoftheoccurencesandtaldistributionlawinasingleframework.Thisglobalstatisticsofextremeeventsiscrucialineldslikeseis-approachwaslaterextendedbyCorral[18,19],wh

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7、perties,itrareextremeeventscanhaveratherstrongordrasticispossibletoanalysethestatisticsofreturnintervalsconsequences

8、makingitwidelyuseful.Onetheoreti-fordierentthresholdsbystudyingonlythebehaviorofcalmotivationforstudyingextremeeventsinaparticu-small uctuationsoccurringveryfrequent

9、ly,whichhavelareldlikenance,istoaccountfortheobservedfatmuchbetterstatisticsandreliabilitythanthoseofthetailsoflog-returns(deviationfromtheNormaldistri-rareextremelarge ucutations.Italsorevealsaspa-butioninthetails)ofstockprices[3].Amorepracti-tiotemporalorganizationoftheseismicit

10、y,assuggestedcalmot