Jos_von_Asmuth_Thesis.pdf - repository

`Ü~éíÉê=P=UU=ëóëíÉãK=qÜÉ=Éëíáã~íÉÇ=é~ê~ãÉíÉêë=çÑ=íÜÉ=åçáëÉ=ãçÇÉä=~êÉ=xα = =OTKVI=σ = =OKQP=Åãz=~åÇ=α = =OVKSI=νσ ν = OKPV=Åãz=Ñçê=íÜÉ=mfocf`q=~åÇ=^oj^=ãçÇÉä=êÉëéÉÅíáîÉäóK=^ë=ï~ë=íÜÉ=Å~ëÉ=ïáíÜ=íÜÉ=êÉ~ä=ïçêäÇ=Ç~í~I=íÜÉ=^oj^=íê~åëÑÉê=ÑìåÅíáçå=ëÜçïë=~=é~êíäó=áêêÉÖìä~ê=é~ííÉêå=~åÇ=áå=íÜáë=Å~ëÉ=ÉîÉå=Ñ~ääë=é~êíäó=çìíëáÇÉ=íÜÉ=ÅçåÑáÇÉåÅÉ=áåíÉêî~ä=çÑ=íÜÉ=mfocf`q=êÉëéçåëÉK=tÜÉå=Åçãé~êáåÖ=íÜÉ=Éëíáã~íÉë=çÑ=ÄçíÜ=ãçÇÉäë=ïáíÜ=íÜÉ=íêìÉ=êÉëéçåëÉ=ÑìåÅíáçå=íÜÉ=ÇÉîá~íáçå=çÑ=íÜÉ=Åçåíáåìçìë=_o=ÑìåÅíáçå=áë=äÉëë=íÜ~å=íÜ~í=çÑ=íÜÉ=ÇáëÅêÉíÉ=íê~åëÑÉê=ÑìåÅíáçåI=~ë=áë=íÜÉ=Å~ëÉ=Ñçê=íÜÉ=é~ê~ãÉíÉêë=çÑ=íÜÉ=åçáëÉ=ãçÇÉäK===3.4 Discussion andconclusionsresponse (−)1.81.61.41.210.80.60.40.2Box−JenkinsPIRFICTTrue response00 200 400 600 800 1000time (in days)=figure 3.8: Transfer functions of a [10 0 1 1 0] [30.4]ARMA model and a PIRFICT model calibrated on thesame simulated series. The dotted lines denote the 95%confidence intervals. The figure illustrates that the partlyirregular shape of the ARMA transfer function is due tooverfitting the data with too high a model order and notconform the ‘true’ response of the synthetic system.qÜÉ=ãÉíÜçÇ=éêÉëÉåíÉÇ=Ü~ë=ëÜçïå=íç=ÅáêÅìãîÉåí=~=åìãÄÉê=çÑ=íÜÉ=äáãáí~íáçåë=çÑ=ÇáëÅêÉíÉ=^oj^=qê~åëÑÉê=cìåÅíáçåJkçáëÉ=ãçÇÉäëK=cáêëíI=íÜÉ=mfocf`q=ãçÇÉä=Å~å=ÄÉ=Å~äáÄê~íÉÇ=çå=Ç~í~=~í=~åó=ÑêÉèìÉåÅó=~î~áä~ÄäÉI=ÄÉÅ~ìëÉ=áí=çéÉê~íÉë=áå=~=Åçåíáåìçìë=íáãÉ=Ççã~áå=~åÇ=íÜÉ=íáãÉ=ëíÉéë=çÑ=íÜÉ=çìíéìí=î~êá~ÄäÉ=~êÉ=åçí=ÅçìéäÉÇ=íç=íÜÉ=íáãÉ=ëíÉéë=çÑ=íÜÉ=áåéìí=î~êá~ÄäÉëK=qÜìëI=~äëç=íÜÉ=ÑêÉèìÉåÅó=çÑ=íÜÉ=áåéìí=ëÉêáÉë=Å~å=ÄÉ=áêêÉÖìä~êK=pÉÅçåÇI=Åçãé~êÉÇ=íç=íÜÉ=ÅçãÄáåÉÇ=^ou=ãçÇÉä=~åÇ=h~äã~å=ÑáäíÉêI=íÜÉ=mfocf`q=ãçÇÉä=çÑÑÉêë=~=ÑìêíÜÉê=ÉñíÉåëáçå=çÑ=íÜÉ=éçëëáÄáäáíáÉë=çÑ=Å~äáÄê~íáåÖ=qck=ãçÇÉäë=çå=áêêÉÖìä~êäó=ëé~ÅÉÇ=íáãÉ=ëÉêáÉëI=ÄÉÅ~ìëÉ=íÜÉ=ëÜ~éÉ=çÑ=íÜÉ=íê~åëÑÉê=ÑìåÅíáçå=áë=åçí=êÉëíêáÅíÉÇ=íç=~å=ÉñéçåÉåíá~äK=qÜáêÇI=ìëáåÖ=íÜÉ=mfocf`q=ãçÇÉäI=íÜÉ=ãçÇÉä=áÇÉåíáÑáÅ~íáçå=éêçÅÉëë=áë=ëáãéäáÑáÉÇ=ÄÉÅ~ìëÉ=íÜÉ=ãçÇÉä=ÑêÉèìÉåÅó=ÇçÉë=åçí=áåíÉêÑÉêÉ=ïáíÜ=íÜÉ=ãçÇÉä=çêÇÉê=~åÇ=é~ê~ãÉíÉê=î~äìÉëI=~åÇ=íÜÉ=ÑäÉñáÄáäáíó=çÑ=~=ëáåÖäÉ=Åçåíáåìçìë=fo=ÑìåÅíáçå=Å~å=ÄÉ=ëìÅÜ=íÜ~í=áí=ÅçãéêáëÉë=~=ê~åÖÉ=çÑ=^oj^=íê~åëÑÉê=ÑìåÅíáçåëK=cìêíÜÉêãçêÉI=íÜÉ=ãçÇÉä=Å~å=ÄÉ=êÉ~Çáäó=áÇÉåíáÑáÉÇ=ìëáåÖ=éÜóëáÅ~ä=áåëáÖÜíK=^äíÜçìÖÜ=íÜÉ=ãÉíÜçÇ=áë=éêÉëÉåíÉÇ=áå=íÜÉ=Ñçêã=çÑ=~=ëáåÖäÉ=áåéìí=qck=ãçÇÉä=Ñçê=íáãÉ=ëÉêáÉë=çÑ=ÖêçìåÇï~íÉê=ÜÉ~ÇI=áí=áë=áå=Ñ~Åí=èìáíÉ=ÖÉåÉê~äI=~åÇ=ÅçìäÇ=ÄÉ=ìëÉÇ=Ñçê=~=î~êáÉíó=çÑ=ëáåÖäÉ=çê=ãìäíá=áåéìíI=EåçåF=ÜóÇêçäçÖáÅ=éêçÄäÉãë=EáKÉK=Ñçê=íÜÉ=ë~ãÉ=éìêéçëÉë=íÜ~í=^oj^=qck=ãçÇÉäë=~êÉ=ìëÉÇI=ëÉÉ=áåíêçÇìÅíáçåFK=qÜÉ=Åçåíáåìçìë=íáãÉ=~ééêç~ÅÜ=éêçÄ~Ääó=çÑÑÉêë=ãçëí=~Çî~åí~ÖÉë=áå=Å~ëÉë=ïÜÉêÉ=íÜÉ=~ÄçîÉ=ãÉåíáçåÉÇ=äáãáí~íáçåë=çÅÅìêI=ïÜÉêÉ=íÜÉ=~å~äóëí=áë=áåíÉêÉëíÉÇ=áå=íÜÉ=ÑìåÅíáçåáåÖ=çÑ=~=ëóëíÉã=çå=ÇáÑÑÉêÉåí=çê=ëã~ää=íáãÉ=ëÅ~äÉëI=áå=íÜÉ=~ìíçã~íÉÇ=~å~äóëáë=çÑ=ä~êÖÉ=èì~åíáíáÉë=çÑ=íáãÉ=ëÉêáÉëI=çê=áå=~ëëÉëëáåÖ=íáãÉ=áåî~êá~åí=êÉëéçåëÉ=ÅÜ~ê~ÅíÉêáëíáÅë=çÑ=ëóëíÉãëK=tÜáäÉ=íÜÉ=mfocf`q=ãçÇÉä=éêçÄ~Ääó=éÉêÑçêãë=ÄÉëí=ïÜÉå=íÜÉ=Çóå~ãáÅ=ÄÉÜ~îáçê=çÑ=~=ëóëíÉã=Å~å=ÄÉ=ÉñéêÉëëÉÇ=áå=íÜÉ=Ñçêã=çÑ=~=ëáãéäÉ=~å~äóíáÅ=Ñçêãìä~I=íÜáë=ëÜçìäÇ=åçí=éçëÉ=~=êÉëíêáÅíáçå=íç=íÜÉ=ìëÉ=çÑ=íÜÉ=ãçÇÉäI=~ë=íÜÉ=ëÜ~éÉ=çÑ=íÜÉ=fo=ÑìåÅíáçå=Å~å=~äëç=ÄÉ=ÖÉåÉê~äáòÉÇ=Äó=ìëáåÖ=ëìãë=çÑ==mfff=ÇÑ=Eçê=çíÜÉêF=ÑìåÅíáçåëK===..…………………………………………………………………………………………….….