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1 ECONOMIC STATISTICS
2 ECONOMIC STATISTICS Sonsored by a Gran TÁMOP /2/A/KMR Course Maerial Develoed by Dearmen of Economics, Faculy of Social Sciences, Eövös Loránd Universiy Budaes (ELTE) Dearmen of Economics, Eövös Loránd Universiy Budaes Insiue of Economics, Hungarian Academy of Sciences Balassi Kiadó, Budaes
3
4 ELTE Faculy of Social Sciences, Dearmen of Economics ECONOMIC STATISTICS Auhor: Anikó Bíró Suervised by Anikó Bíró June 200
5 ECONOMIC STATISTICS Week AR models Anikó Bíró
6 AR() model U o now: AR() model Sloe saionariy AR() model: auoregression of order ρ=0 uni roo -2<ρ<0 - saionary e e
7 AR() model modified form e e
8 Uni roo has a uni roo canno be included in he regression! Exemion: coinegraion Differenced value (Δ) has o be used! Δ sacionary difference saionary : has sochasic rend
9 Deerminisic rend Examle: e, saionary rend saionary Grah: similar o sochasic rend no enough o make a decision on uni roo
10 Examle AR(4) model AR(4) model wih deerminisic rend: Generae differenced variables Differenced variables: 3 lags Coefficien of - = 0? e
11 Seasonaliy Paern recurring a regular inervals Examle: consumion, agriculural roducion, exor Treamen: variables indicaing seasonaliy Quarerly: 3 dummies! Monhly: dummies! Or: seasonal adjusmen KSH: seasonally adjused ime series
12 Secificaion choice... e Maximal lag lengh ( max ) Esimae AR( max ) model wih or wihou deerminisic rend (according o he deenden variable, based on assumion!) Tes Γ max- =0 (-es) if saisfied: decrease lag lengh by one
13 Uni roo es Tesing ρ=0: usual -es canno be used! Dickey Fuller-es: use -saisic, bu criical values are correced Problem: weak es can find uni roo even if i is no resen Examle: rend saionary ime series, srucural break
14 Dickey Fuller-es Quesion: include rend? Null hyohesis: uni roo Large -value: has uni roo, no saionary
15 Uni roo es examle Monly exor daa Seasonally adjused Trend Null Hyohesis: EXPORT_SA has a uni roo Exogenous: Consan, Linear Trend Lag Lengh: 3 (Auomaic based on SIC, MAXLAG=3) -Saisic Prob. Augmened Dickey Fuller-es sa. -2,86 0,530 Tes criical values: % level -4,080 5% level -3,4389 0% level -3,438
16 Summary AR() model, modified form Uni roo in AR() models Trend saionariy Seasonaliy Dickey Fuller-es
17 AR models Seminar
18 AR() model AR() model: auoregression of order ρ=0 uni roo -2<ρ<0 - saionary e e
19 Uni roo has a uni roo canno be included in he regression! Exemion: coinegraion Differenced value (Δ) has o be used! Δ saionary difference saionary : has sochasic rend
20 Examle monhly exor MNB daa (m EUR) Esimaion of AR(4) model wih deerminisic rend: Generae differenced variables Differenced variables: 3 lags Coefficien of - = 0? e
21 Seasonaliy Paern recurring a regular inervals Treamen: variables indicaing seasonaliy Quarerly: 3 dummies Monhly: dummies
22 Seasonaliy examle Monhly exor daa 2 seasonal dummies: mulicollineariy EViews error message EViews: Procs/Seasonal adjusmen
23 Secificaion choice... e Maximal lag lengh ( max ) Esimae AR( max ) mode wih or wihou deerminisic rend Tes Γ max- =0 (-es) if saisfied: decrease lag lengh by one Tes he significance of rend afer lag lengh selecion Examle: AR() model for firs differenced log exor ime series (use seasonally adjused daa!)
24 Dickey Fuller-es Tes uni roo View/Uni roo es Oion: auomaic lag lengh selecion Quesion: include rend? Null hyohesis: uni roo Large -value: has uni roo, no saionary
25 Uni roo es Monhly exor daa (MNB) Seasonally adjused Trend? Inerre ouu Is he differenced variable saionary? Quarerly ublic deb daa (MNB) Trend?
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