Основни знания
Atimeseriesisasequenceofnumbersinchronologicalorder.
Характеристики на меки сериали:
1.Arealisticandtruesetofdata,notobtainedthroughexperimentsinmathematicalstatistics.Sinceitistrue,itisastatisticalindicatorthatreflectsacertainphenomenon.Therefore,behindthetimeseriesisthelawofchangeofacertainphenomenon.
2.Динамични данни.
Основните стъпки на моделирането на времеви серии са:
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.
Характеристики
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.
Характеристики: прост и лесен за използване, лесен за управление, но слаба точност, като цяло подходящ само за краткосрочни прогнози.
Класификация
Accordingtoitscharacteristics,thetimeserieshasthefollowingmanifestations,andproducescorrespondinganalysismethods:
1.Long-termtrendchanges:Affectedbyacertainbasicfactor,thedatashowsacertaintendencywhenitchangesovertime,anditsteadilyincreasesordecreasesaccordingtoacertainrule.Theanalysismethodsusedare:movingaveragemethod,exponentialsmoothingmethod,modelfittingmethod,etc.
2.Seasonalcyclechanges:Affectedbyfactorssuchasseasonalchanges,thesequencechangesregularlyaccordingtoafixedcycle,alsoknownasthebusinesscycle.Methodused:seasonalindex.
3. Циклични промени: променливи промени с нередовни цикли.
4. Случайни промени: Промени в последователността, причинени от много несигурни фактори.
Timeseriesanalysismainlyincludesdeterministicchangeanalysisandrandomchangeanalysis.Amongthem,thedeterministicchangeanalysisincludestrendchangeanalysis,cyclechangeanalysis,andcyclechangeanalysis.Анализ на случайни промени:AR,MA,ARMAmodels,etc.
Специфични методи
Детерминистичен анализ на времеви редове
Thepurposeofdeterministictimeseriesanalysis:toovercometheinfluenceofotherfactors,simplymeasureacertaindeterministicfactoronthesequenceTheinfluenceofvariousdeterministicfactorsandtheircomprehensiveinfluenceonthesequenceareinferred.
Thepurposeoftimeseriestrendanalysis:Sometimeserieshaveverysignificanttrends.Thepurposeofouranalysisistofindthistrendinthesequenceandusethistrendtomakereasonablepredictionsforthedevelopmentofthesequence.
Commonmethods:trendfittingmethodandsmoothingmethod.
Thetrendfittingmethodistousetimeastheindependentvariableandthecorrespondingsequenceobservationvalueasthedependentvariabletoestablisharegressionmodelofthesequencevaluechangingwithtime.Includinglinearfittingandnonlinearfitting.
Theuseoccasionoflinearfittingistheoccasionwherethelong-termtrendshowslinearcharacteristics.Theparameterestimationmethodisleastsquareestimation.
Темоделис,,.
Theuseoccasionsofnonlinearfittingareoccasionswherethelong-termtrendshowsnon-linearcharacteristics.Theideaofparameterestimationistoconverteverythingthatcanbeconvertedintoalinearmodelintoalinearmodel,andusethelinearleastsquaremethodtoestimatetheparameters.Ifitcan'tbeconvertedtolinear,useiterativemethodtoestimatetheparameters.
Моделите включват,,,и др.
Smoothingmethodisacommonlyusedmethodfortrendanalysisandforecasting.Itusessmoothingtechnologytoweakentheinfluenceofshort-termrandomfluctuationsonthesequenceandsmooththesequence,therebyshowingthelawoflong-termtrendchanges.
Метод за прогнозиране на времеви редове
Метод за прогнозиране на времеви редовеcanbeusedforshort-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.
Анализ на случайни промени
Therandomtimeseriesmodel(timeseriesmodeling)referstoamodelbuiltusingonlyitspastvaluesandrandomdisturbanceterms,anditsgeneralformis.Takethelinearequation,theone-periodlag,andthewhitenoiserandomdisturbanceterm().
Моделът ще бъде авторегресивен процес от първи ред AR(1):.Тук конкретно се отнася до белия шум.
Общият авторегресивен процес AR(p) на реда на p е.
Ако терминът на случайно смущение е бял шум(), тогава формулата(1) се нарича чист AR(p)процес(чист AR(p)процес), означен като.
Ако няма бял шум, обикновено се счита, че процесът на движеща се средна стойност от порядъка на q MA(q):.
Комбинирайте pureAR(p) с pureMA(q)заедно с общ авторегресивен пълзящ среден(aunoregressivemovingaverage)процес ARMA(p,q):.
Формулата показва:
1.Arandomtimeseriescanbegeneratedbyanautoregressivemovingaverageprocess,thatis,theseriescanbegeneratedbyitsownpastorlagvalueandrandomdisturbancetermsToexplain.
2.Ifthesequenceisstationary,thatis,itsbehaviordoesnotchangeovertime,thenwecanpredictthefuturethroughthepastbehaviorofthesequence.Thisisexactlytheadvantageoftherandomtimeseriesanalysismodel.ItshouldbenotedthatnoneoftheaboveARMA(p,q)modelscontainsaconstantterm.Ifaconstanttermisincluded,theconstanttermdoesnotaffecttheoriginalpropertiesofthemodel,becausethemodelcontainingtheconstanttermisconvertedtothemodelwithouttheconstanttermthroughappropriatedeformation.
Основни употреби
Timeseriesanalysisiscommonlyusedinthemacro-controlofthenationaleconomy,regionalcomprehensivedevelopmentplanning,businessmanagement,marketpotentialprediction,meteorologicalforecast,hydrologicalforecast,earthquakeprecursorforecast,Croppestsanddiseasesforecast,environmentalpollutioncontrol,ecologicalbalance,astronomyandoceanography.Itmainlyincludesresearchandanalysisfromthefollowingaspects.
Описание на системата
Accordingtothetimeseriesdataobtainedfromtheobservationofthesystem,thecurvefittingmethodisusedtoobjectivelydescribethesystem.
Системен анализ
Whentheobservationsaretakenfrommorethantwovariables,thechangesinonetimeseriescanbeusedtoexplainthechangesintheothertimeseries,Soastogaininsightintothemechanismofagiventimeseries.
Предсказвай бъдещето
Generally,theARMAmodelisusedtofitthetimeseriestopredictthefuturevalueofthetimeseries.
Решение и контрол
Accordingtothetimeseriesmodel,theinputvariablescanbeadjustedtokeepthesystemdevelopmentprocessatthetargetvalue,thatis,whentheprocessispredictedtodeviatefromthetargetThenecessarycontrolcanbecarriedout.