ECONOMIC STATISTICS. Sponsored by a Grant TÁMOP /2/A/KMR Course Material Developed by Department of Economics,

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1 ECONOMIC STATISTICS Sonsord by a Gran TÁMOP /2/A/KMR Cours Marial Dvlod by Darmn of Economics, Faculy of Social Scincs, Eövös Loránd Univrsiy Budas (ELTE) Darmn of Economics, Eövös Loránd Univrsiy Budas Insiu of Economics, Hungarian Acadmy of Scincs Balassi Kiadó, Budas

2 2 Auhor: Anikó Bíró Survisd by Anikó Bíró Jun 200 Wk AR modls AR() modl U o now: AR() modl Slo saionariy AR() modl: auorgrssion of ordr ρ=0 uni roo -2<ρ<0 - saionary

3 3 AR() modl modifid form 2 2 Uni roo has a uni roo canno b includd in h rgrssion! Exmion: coingraion Diffrncd valu (Δ) has o b usd! Δ sacionary diffrnc saionary : has sochasic rnd Drminisic rnd Examl:, saionary rnd saionary Grah: similar o sochasic rnd no nough o mak a dcision on uni roo

4 Examl AR(4) modl AR(4) modl wih drminisic rnd: Gnra diffrncd variabls Diffrncd variabls: 3 lags Cofficin of - = 0? Sasonaliy Parn rcurring a rgular inrvals Examl: consumion, agriculural roducion, xor Tramn: variabls indicaing sasonaliy Quarrly: 3 dummis! Monhly: dummis! Or: sasonal adjusmn KSH: sasonally adjusd im sris Scificaion choic Maximal lag lngh ( max ) Esima AR( max ) modl wih or wihou drminisic rnd (according o h dndn variabl, basd on assumion!) Ts Γ max- =0 (-s) if saisfid: dcras lag lngh by on 4

5 Tsing ρ=0: usual -s canno b usd! Uni roo s Dicky Fullr-s: us -saisic, bu criical valus ar corrcd Problm: wak s can find uni roo vn if i is no rsn Examl: rnd saionary im sris, srucural brak Qusion: includ rnd? Dicky Fullr-s Null hyohsis: uni roo Larg -valu: has uni roo, no saionary Uni roo s xaml Monly xor daa Sasonally adjusd Trnd Null Hyohsis: EXPORT_SA has a uni roo Exognous: Consan, Linar Trnd Lag Lngh: 3 (Auomaic basd on SIC, MAXLAG=3) -Saisic Prob. Augmnd Dicky Fullr-s sa. -2,86 0,530 Ts criical valus: % lvl -4,080 5% lvl -3,4389 0% lvl -3,438 5

6 Summary AR() modl, modifid form Uni roo in AR() modls Trnd saionariy Sasonaliy Dicky Fullr-s AR modls Sminar AR() modl AR() modl: auorgrssion of ordr ρ=0 uni roo -2<ρ<0 - saionary Uni roo has a uni roo canno b includd in h rgrssion! Exmion: coingraion Diffrncd valu (Δ) has o b usd! 6

7 Δ saionary diffrnc saionary : has sochasic rnd Examl monhly xor MNB daa (m EUR) Esimaion of AR(4) modl wih drminisic rnd: Gnra diffrncd variabls Diffrncd variabls: 3 lags Cofficin of - = 0? Sasonaliy Parn rcurring a rgular inrvals Tramn: variabls indicaing sasonaliy Quarrly: 3 dummis Monhly: dummis Sasonaliy xaml Monhly xor daa 2 sasonal dummis: mulicollinariy EViws rror mssag EViws: Procs/Sasonal adjusmn 7

8 Scificaion choic Maximal lag lngh ( max ) Esima AR( max ) mod wih or wihou drminisic rnd Ts Γ max- =0 (-s) if saisfid: dcras lag lngh by on Ts h significanc of rnd afr lag lngh slcion Examl: AR() modl for firs diffrncd log xor im sris (us sasonally adjusd daa!) Dicky Fullr-s Ts uni roo Viw/Uni roo s Oion: auomaic lag lngh slcion Qusion: includ rnd? Null hyohsis: uni roo Larg -valu: has uni roo, no saionary Uni roo s Monhly xor daa (MNB) Sasonally adjusd Trnd? Inrr ouu Is h diffrncd variabl saionary? Quarrly ublic db daa (MNB) Trnd? 8