The Effects of the Irregular Sample and Missing Data in Time Series Analysis

Humanself-reporttimeseriesdataaretypicallymarkedbyirregularitiesin samplingrates;furthermore,theseirregularitiesaretypicallynaturaloutcomesofthedatagenerationprocess.Relativelylittlehasbeenpublished toassisttheanalysisofirregularlysampleddata.Wereporttheresultsof aseriesofcomputationalexperimentsonsyntheticdatasetsdesignedto assesstheutilityoftechniquesforhandlingirregulartimeseriesdata.The behaviorofaconservativequasiperiodic,adissipativechaotic,andaselforganizedcriticaldynamicsweresampledregularlyintime,andtheregular samplingwasdisruptedbydatapointremovalorbystochasticshiftsintime. Missingdatasegmentswerethenpatchedbymeansofsegmentconcatenation,bysegment‡llingwithaveragedatavalues,orbylocalinterpolationin phasespace.Wecomparedresultsofnonlinearanalyticaltools,suchasautocorrelationsandcorrelationdimensions,usingcompleteandpatchedsets,as wellaspowerspectrawithLombperiodogramsofthedecimatedsets.Local interpolationinphasespacewasparticularlysuccessfulatpreservingkeyCONTENTSMethods ................................................................................................................ 137 Time Series Length ......................................................................................... 137 Dynamics ......................................................................................................... 138 Patching the Decimated Time Series ........................................................... 141 Time Series Analysis ...................................................................................... 142Results ................................................................................................................... 144 Effects of Missing Points and Temporal Inaccuracy ................................. 144 Correlation Dimension .................................................................................. 147Discussion ............................................................................................................ 153 Acknowledgments .............................................................................................. 155 References ............................................................................................................. 155featuresoftheoriginaldata,butrequiredpotentiallyimpracticalquantities ofintactdataasaprimer.Whiletheotherpatchingmethodsarenotlimited bytheneedforintactdata,theydistortresultsrelativetotheintactseries. Weconcludethatirregularlysampleddatasetswithasmuchas15%missing datacanpotentiallyberesampledorrepairedforanalysiswithtechniques that assume regular sampling without introducing substantial errors.