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On robust ESACF identification of mixed ARIMA models

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  • Hella, Heikki

Abstract

Tilastoaineistossa on usein joitakin havaintoja, jotka poikkeavat merkittävästi aineiston muusta osasta.Nämä poikkeavat havainnot (outlierit) aiheuttavat huomattavia ongelmia tilastollisessa analyysissä ja päättelyssä.Valitettavasti monet klassisen tilastotieteen menetelmät, kuten tavallinen pienimmän neliösumman menetelmä, ovat hyvin herkkiä näiden poikkeavien havaintojen vaikutuksille, eli ne eivät ole robusteja.Lineaarisille regressiomalleille ja viime aikoina myös aikasarjamalleille on kuitenkin kehitetty useita robusteja estimointi- ja diagnostiikkamenetelmiä.Aikasarjamallien robustia täsmentämistä koskeva kirjallisuus ei ole vielä kovin laajaa, mutta kasvaa nopeasti.Mallien täsmentäminen on hankala juttu robustissa aikasarjaanalyysissä (Martin ja Yohai 1986).Jos aikasarjan tiedetään tai oletetaan sisältävän poikkeavia havaintoja, mallintamisen ensi vaihe pitäisi suorittaa robustein täsmentämismenetelmin. Robustin version kehittäminen niin sanotusta laajennetusta autokorrelaatiofunktiomenetelmästä (EACF-proseduuri), jonka alun perin kehittivät Tsay ja Tiao (1984) yhden muuttujan ARIMAmallien alustavaksi täsmentämiseksi, ja robustin menetelmän tulosten vertailu perinteisen menetelmän antamiin tuloksiin. 2.Laajennetun autokorrelaatiofunktion kertoimien (eli ESACF -matriisin elementtien) otosjakaumien simulointi klassisin ja robustein menetelmin sekä puhtaiden että outliereillä saastuneiden aikasarjojen tapauksissa. 3.Laajennetun autokorrelaatiofunktion kertoimille simuloitujen keskivirheiden vertaaminen teoreettisiin estimaatteihinsa. Robustointi koskee kahta ESACF-proseduurin vaihetta: iteratiivista autoregressiota, AR(p), ja autokorrelaatiofunktiota, jota käytetään vähemmän harhaisten estimaattien tuottamiseksi.Simulointikokeiden lisäksi robusteja versioita ESACF-proseduurista sovelletaan työssä eräisiin synteettisiin ja aitoihin aikasarjoihin, joista muutamia on kirjallisuudessa käytetty havainnollisina esimerkkeinä. Simulointikokeet osoittavat, että koska robusti MM-estimaattori on tehokas myös outliereitä sisältämättömien aikasarjojen tapauksissa, tätä robustia ESACF-proseduuria voidaan aina soveltaa. Menetelmästä saatava tuki robustiin yksikköjuuritestaukseen on ilmeinen, mutta vaatii lisää tutkimusta. Avainsanat: robusti täsmentäminen, robusti laajennettu autokorrelaatiofunktio, outlieri, robusti regressioestimointi, Monte Carlo -simulointi, aikasarjamallit

Suggested Citation

  • Hella, Heikki, 2003. "On robust ESACF identification of mixed ARIMA models," Bank of Finland Scientific Monographs, Bank of Finland, volume 0, number sm2003_027.
    • Handle: RePEc:zbw:bofism:sm2003_027
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    References listed on IDEAS

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