Perustieto
Atimeseriesisasequenceofnumbersinchronologicalorder.
Aikasarjan ominaisuudet:
1.Arealisticandtruesetofdata,notobtainedthroughexperimentsinmathematicalstatistics.Sinceitistrue,itisastatisticalindicatorthatreflectsacertainphenomenon.Therefore,behindthetimeseriesisthelawofchangeofacertainphenomenon.
2. Dynaamiset tiedot.
Timeseries-mallinnuksen perusvaiheet ovat:
1.Obtainthetimeseriesdynamicdataoftheobservedsystembymethodssuchasobservation,survey,statistics,andsampling.
2.Drawcorrelationgraphsbasedondynamicdata,conductcorrelationanalysis,andfindautocorrelationfunction.Thecorrelationdiagramcanshowthetrendandcycleofchanges,andcanfindjumppointsandinflectionpoints.Jumppointsareobservationsthatareinconsistentwithotherdata.Ifthejumppointisthecorrectobservationvalue,itshouldbetakenintoaccountwhenmodeling,ifitisanabnormalphenomenon,thejumppointshouldbeadjustedtotheexpectedvalue.Theinflectionpointisthepointatwhichthetimeseriessuddenlychangesfromanupwardtrendtoadownwardtrend.Ifthereisaninflectionpoint,differentmodelsmustbeusedtofitthetimeseriessegmentallyduringmodeling,suchasathresholdregressionmodel.
3.Identifyasuitablerandommodelandperformcurvefitting,thatis,useageneralrandommodeltofittheobservationdataofthetimeseries.Forshortorsimpletimeseries,trendmodelsandseasonalmodelspluserrorscanbeusedforfitting.Forstationarytimeseries,generalARMAmodel(autoregressivemovingaveragemodel)anditsspecialcaseautoregressivemodel,movingaveragemodelorcombined-ARMAmodelcanbeusedforfitting.Whentherearemorethan50observations,theARMAmodelisgenerallyused.Fornon-stationarytimeseries,theobservedtimeseriesmustbefirstdifferentiatedintoastationarytimeseries,andthenanappropriatemodelisusedtofitthedifferenceseries.
Ominaisuudet
Timeseriesanalysisisoneofthequantitativeforecastingmethods.Itincludesgeneralstatisticalanalysis(suchasautocorrelationanalysis,spectrumanalysis,etc.),theestablishmentandinferenceofstatisticalmodels,andtheoptimalprediction,controlandfilteringoftimeseries.Classicalstatisticalanalysisassumestheindependenceofdataseries,whiletimeseriesanalysisfocusesontheinterdependenceofdataseries.Thelatterisactuallyastatisticalanalysisoftherandomprocessofdiscreteindicators,soitcanberegardedasacomponentofrandomprocessstatistics.Forexample,therainfallofthefirstmonth,thesecondmonth,...,theNthmonthinacertainareaisrecorded,andtherainfallinthefuturemonthscanbeforecastedbyusingthetimeseriesanalysismethod.
Basicidea:Basedonthesystem'slimited-lengthoperatingrecords(observationdata),establishamathematicalmodelthatcanmoreaccuratelyreflectthedynamicdependenciescontainedinthesequence,anduseittopredictthefutureofthesystem.
Basicprinciples:Oneistorecognizethecontinuityofthedevelopmentofthings.Usingpastdata,wecaninferthedevelopmenttrendofthings.Thesecondistoconsidertherandomnessofthedevelopmentofthings.Thedevelopmentofanythingmaybeaffectedbyaccidentalfactors.Forthisreason,theweightedaveragemethodinstatisticalanalysisshouldbeusedtoprocesshistoricaldata.
Ominaisuudet: yksinkertainen ja helppokäyttöinen, helppokäyttöinen, mutta huono tarkkuus, sopii yleensä vain lyhyen aikavälin ennusteisiin.
Luokittelu
Accordingtoitscharacteristics,thetimeserieshasthefollowingmanifestations,andproducescorrespondinganalysismethods:
1.Long-termtrendchanges:Affectedbyacertainbasicfactor,thedatashowsacertaintendencywhenitchangesovertime,anditsteadilyincreasesordecreasesaccordingtoacertainrule.Theanalysismethodsusedare:movingaveragemethod,exponentialsmoothingmethod,modelfittingmethod,etc.
2.Seasonalcyclechanges:Affectedbyfactorssuchasseasonalchanges,thesequencechangesregularlyaccordingtoafixedcycle,alsoknownasthebusinesscycle.Methodused:seasonalindex.
3. Jaksojen muutokset: vaihtelevat muutokset epäsäännöllisillä jaksoilla.
4.Satunnaiset muutokset:Monen epävarman tekijän aiheuttamat sekvenssimuutokset.
Timeseriesanalysismainlyincludesdeterministicchangeanalysisandrandomchangeanalysis.Amongthem,thedeterministicchangeanalysisincludestrendchangeanalysis,cyclechangeanalysis,andcyclechangeanalysis.Satunnaismuutosanalyysi:AR,MA,ARMAmodels,etc.
Tietyt menetelmät
Deterministinen aikasarjaanalyysi
Thepurposeofdeterministictimeseriesanalysis:toovercometheinfluenceofotherfactors,simplymeasureacertaindeterministicfactoronthesequenceTheinfluenceofvariousdeterministicfactorsandtheircomprehensiveinfluenceonthesequenceareinferred.
Thepurposeoftimeseriestrendanalysis:Sometimeserieshaveverysignificanttrends.Thepurposeofouranalysisistofindthistrendinthesequenceandusethistrendtomakereasonablepredictionsforthedevelopmentofthesequence.
Commonmethods:trendfittingmethodandsmoothingmethod.
Thetrendfittingmethodistousetimeastheindependentvariableandthecorrespondingsequenceobservationvalueasthedependentvariabletoestablisharegressionmodelofthesequencevaluechangingwithtime.Includinglinearfittingandnonlinearfitting.
Theuseoccasionoflinearfittingistheoccasionwherethelong-termtrendshowslinearcharacteristics.Theparameterestimationmethodisleastsquareestimation.
Malli,,.
Theuseoccasionsofnonlinearfittingareoccasionswherethelong-termtrendshowsnon-linearcharacteristics.Theideaofparameterestimationistoconverteverythingthatcanbeconvertedintoalinearmodelintoalinearmodel,andusethelinearleastsquaremethodtoestimatetheparameters.Ifitcan'tbeconvertedtolinear,useiterativemethodtoestimatetheparameters.
Mallit sisältävät,,, jne.
Smoothingmethodisacommonlyusedmethodfortrendanalysisandforecasting.Itusessmoothingtechnologytoweakentheinfluenceofshort-termrandomfluctuationsonthesequenceandsmooththesequence,therebyshowingthelawoflong-termtrendchanges.
Aikasarjaennustemenetelmä
Aikasarjaennustemenetelmäcanbeusedforshort-termforecasting,mid-termforecastingandlong-termforecasting.Accordingtothedifferentmethodsofdataanalysis,itcanbefurtherdividedinto:simplesequentialtimeaveragemethodandweightedsequentialtimeaveragemethod.
Simpleaveragemethod:alsoknownasarithmeticaveragemethod.Thatis,thestatisticalvaluesofanumberofhistoricalperiodsaretakenastheobservedvalues,andthearithmeticaverageiscalculatedasthepredictedvalueforthenextperiod.Thismethodisbasedonthefollowinghypothesis:"Itwasthesameinthepast,anditwillbethesameinthefuture."Itequatesandaveragesshort-termandlong-termdata,soitcanonlybeappliedtotrendforecastswherethingshavenotchangedmuch.Ifthingsshowacertainupwardordownwardtrend,thismethodshouldnotbeused.
Weightedaveragemethod:weightthehistoricaldataofeachperiodaccordingtothedegreeofshort-termandlong-terminfluence,andcalculatetheaveragevalueasthenextforecastvalue.
Satunnaismuutosanalyysi
Therandomtimeseriesmodel(timeseriesmodeling)referstoamodelbuiltusingonlyitspastvaluesandrandomdisturbanceterms,anditsgeneralformis.Takethelinearequation,theone-periodlag,andthewhitenoiserandomdisturbanceterm().
Malli on ensimmäisen asteen autoregressiivinen prosessiAR(1):.Tässä viittaa erityisesti valkoiseen kohinaan.
Yleinenp-järjestysautoregressiivinen prosessiAR(p) on.
Jos satunnainen häiriötermi on whitenoise(),niin kaavaa (1) kutsutaan puhtaastiAR(p)prosessiksi(puhdasAR(p)prosessiksi).
Jos ei ole valkoista kohinaa, sen katsotaan yleensä olevan q-tilauskeskimääräinen prosessiMA(q):.
Yhdistä PureMA(q):n kanssa yleinen autoregressiivinen liikkuvakeskiarvo(anoregressiivinenliikkuvakeskiarvo)prosessiARMA(p,q):.
Kaava näyttää:
1.Arandomtimeseriescanbegeneratedbyanautoregressivemovingaverageprocess,thatis,theseriescanbegeneratedbyitsownpastorlagvalueandrandomdisturbancetermsToexplain.
2.Ifthesequenceisstationary,thatis,itsbehaviordoesnotchangeovertime,thenwecanpredictthefuturethroughthepastbehaviorofthesequence.Thisisexactlytheadvantageoftherandomtimeseriesanalysismodel.ItshouldbenotedthatnoneoftheaboveARMA(p,q)modelscontainsaconstantterm.Ifaconstanttermisincluded,theconstanttermdoesnotaffecttheoriginalpropertiesofthemodel,becausethemodelcontainingtheconstanttermisconvertedtothemodelwithouttheconstanttermthroughappropriatedeformation.
Pääkäyttäjät
Timeseriesanalysisiscommonlyusedinthemacro-controlofthenationaleconomy,regionalcomprehensivedevelopmentplanning,businessmanagement,marketpotentialprediction,meteorologicalforecast,hydrologicalforecast,earthquakeprecursorforecast,Croppestsanddiseasesforecast,environmentalpollutioncontrol,ecologicalbalance,astronomyandoceanography.Itmainlyincludesresearchandanalysisfromthefollowingaspects.
Järjestelmän kuvaus
Accordingtothetimeseriesdataobtainedfromtheobservationofthesystem,thecurvefittingmethodisusedtoobjectivelydescribethesystem.
Järjestelmäanalyysi
Whentheobservationsaretakenfrommorethantwovariables,thechangesinonetimeseriescanbeusedtoexplainthechangesintheothertimeseries,Soastogaininsightintothemechanismofagiventimeseries.
Ennusta tulevaisuutta
Generally,theARMAmodelisusedtofitthetimeseriestopredictthefuturevalueofthetimeseries.
Päätös ja valvonta
Accordingtothetimeseriesmodel,theinputvariablescanbeadjustedtokeepthesystemdevelopmentprocessatthetargetvalue,thatis,whentheprocessispredictedtodeviatefromthetargetThenecessarycontrolcanbecarriedout.