Econometrie avansata ppt

8/13/2019 Econometrie avansata ppt

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Econometrie Avansata

Dr. Adrian Codirlasu, CFA

Dr. Bogdan Moinescu


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Definitie

O secventa de valori inregistrate de o

variabila aleatoare specifica intr-o anumita

perioada de timp


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Caracteristici

Frecventa

Populatie vs. esantion

Momente Stationaritate

Sezonalitate


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Frecventa

Reprezinta periodicitatea cu care este observat

variabila.

Functie de specificul seriei de timp, frecventapoate fi zilnica (cum este cazul preturilor

activelor financiare cursurile actiunilor, ratele

de dobanda, cursul de schimb), lunara (de

exemplu, rata inflatiei, salariul mediu peeconomie, rata somajului), trimestriala (cum este

produsul intern brut) sau anuala


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Momentele seriei de timp

Media

Varianta

Coeficientul de asimetrie (skewness)

Kurtosis


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Stationaritate

Conditiile ce trebuie indeplinite pentru ca o

serie de timp s fie stationara sunt:

media seriei de timp sa fie constanta sau cu

alte cuvinte, observatiile trebuie sa fluctuezein jurul mediei.

varianta seriei s fie constanta.

Din punct de vedere economic, o serieeste stationara daca un soc asupra seriei

este temporar (se absoarbe in timp) si nu

permanent.


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Stationaritate

In cazul in care seria nu este stationara,

prin diferentiere, se obtine o serie

stationara.

Ordinul de integrare al seriei reprezinta

numarul de diferentieri succesive

necesare pentru obtinerea unei serii

stationare (sau numarul de radaciniunitare al seriei).


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Sezonalitate

Seriile de timp cu frecventa lunara sau

trimestriala prezinta adesea evoluaii care

au o anumita ciclicitate. De exemplu

activitatea economica se incetineste inlunile de iarna, preturile cresc mai mult n

lunile reci decat in perioada de vara etc.

In analiza econometrica, pentru a eliminaaceste evolutii sezoniere seriile de timp

sunt ajustate sezonier.


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II. Teste statistice


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II.1. Distributii


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Distributia de probabilitate

Este reprezentarea tuturor valorilor pe

care le poate lua o variabil aleatore si a

probabilitii de apariie a acestor valori

Variabile aleatoare

Discrete

Continue


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Distributii

Normala

Lognormala

t

Chi patrat

F


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Distributia normala


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Distributia log-normala


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Distributia t


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Distributia Chi-patrat


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Distributia F


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II.2. Testarea ipotezelor


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Testarea ipotezelor

Definirea ipotezei;

Identificarea testului statistic ce va fi utilizat i a

distribuiei de probabilitate a acestuia;

Specificarea nivelului de relevan al testului;

Specificarea regulii de decizie;

Colectarea datelor i estimarea parametrului;

Luarea deciziei statistice;

Luarea deciziei economice.


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Definirea ipotezei Specificarea ipotezei nule i a ipotezei

alternative

Ipoteza nul, notat cu , reprezint ipoteza ce

este testat, iar ipoteza alternativ, notat cu ,este ipoteza acceptat n cazul n care ipoteza

nul este respins


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Testarea mediei

Esantion mare(n > 30)

Esantion mic(n < 30)

Populatia are o distributie normala Testul tsau testul z Testul t

Populatia nu are o distr ibutie normala Testul t sau testul z Nu se poate testa


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Testarea variantei

cu n 1grade de libertate

varianta esantionului de date utilizat


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III. Analiza seriilor de

timp in EViews


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Crearea unui fisier de lucru


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Definirea seriilor


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Introducerea datelor


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Prelucrea seriilor


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Stationaritatea seriilor de timp

Teste statisticeAugmented Dickey-Fuller (ADF)

Phillips-Perron


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Testarea stationaritatii seriei


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Interpretarea rezultatului

statisticNull Hypothesis: L_EUR has a unit root

Exogenous: Constant, Linear Trend

Lag Length: 3 (Automatic based on SIC, MAXLAG=25)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -0.981155 0.9448

Test critical values: 1% level -3.962327

5% level -3.411905

10% level -3.127850


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Analiza distributiei seriei


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Serie normal distribuita

Coeficientul de asimetrie (skewness) este zero

distributia normala este simetrica.

Kurtotica (kurtosis) este 3. Dac acest indicator

are o valoare mai mare dect 3, atunci distributiase numete leptokurtotica, iar daca acesta este

mai mic dect 3 atunci distributia se numeste

platikurtotica.


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Distributie EURRON

-12

-8

-4

0

4

8

12

-.08 -.04 .00 .04 .08

DL_EUR

NormalQuantile

Theoretical Quantile-Quantile

0

20

40

60

80

100

-.04 -.02 .00 .02 .04 .06

DL_EUR

Kernel Density (Epanechnikov, h = 0.0018)


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Functia de autocorelatie


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Trendul seriilor de timp


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Filtrul Hodrick-Prescott


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Ajustarea sezoniera

a seriilor de timp


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Investigarea sezonalitatii


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Proceduri de desezonalizare

Census X12

Census X11

Tramo/Seats


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Proceduri de desezonalizare


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Serie desezonalizata


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IV. Regresia liniara

multipla


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Utilizare Cu ajutorul regresiei liniare multiple, se poate

determina impactul pe care il au mai multe

variabile independente asupra unei anumite

variabile (numita variabila dependenta)


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Ecuatia de regresie


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Determinarea elasticitatilor

Daca variabila dependenta si variabilele

independente sunt specificate in logaritmi

naturali, atunci coeficientii variabilelor

independente pot fi interpretati caelasticitati

Astfel, acesti coeficienti vor arata cu cat la

suta se modifica variabila dependentadaca variabila independenta se modifica

cu 1 la suta


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Ipotezele regresiei liniare

Legtura dintre variabila dependent ivariabilele independente este liniar

Variabilele independente sunt aleatoare.

Intre variabilele independente incluse intr-o regresie nu exista nici o relatie liniara.

Valoarea ateptat a termenului de eroare

este 0


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Ipotezele regresiei liniare

Varianta termenului de eroare esteaceeasi pentru toate observaiile(erori

homoskedastice).

Termenul de eroare este necorelat intreobservatii.

Termenul de eroare este normal distribuit.


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Impactul incalcarii ipotezelor

Heteroskedasticitate Erorile standard ale regresiei sunt incorecte

Corelaieseriala erorilor Erorile standard ale regresiei sunt incorecte

Multicoliniaritate Valori mari ale lui R-patrat si valori mici ale valorilort-statisticale coeficientilor variabilelor independente


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Teste statitistice

pentru regresia liniara

R-patrat

R-patrat ajustat (cu numarul de variabileindependente incluse in regresie)

Criterii informationale

Durbin-Watson


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Teste statitistice

pentru regresia liniara Teste pentru coeficientii obtinuti din

ecuatia de regresie

Testul tpentru testarea individuala a

coeficietilor

Testul Fpentru testarea tuturor coeficientilor

Testul Wald


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Teste statitistice

pentru regresia liniara Teste pentru erorile ecuatiei de regresie

Corlograma erorilorCorelograma erorilor patratice

Testarea distributiei erorilor (testul Jarque-

Berra)


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Regresii cu variabile calitative

Variabile dummyAcestea iau valoarea 1 dac o anumita conditie este

adevarata si valoarea 0 in caz contrar

Numarul de variabile dummyeste cu 1 mai mic decat

numarul de conditii, in caz contrat existandmulticoliniaritate

Variabilele dummypot fi utilizate si pentru captareaimpactului sezonier asupra variabilei independente,

introducand cel mult 11 variabile dummypentrudatele cu frecven lunara sau cel mult 3 variabiledummypentru datele cu frecventa trimestriala, incazul in care datele nu au fost ajustate sezonier inprealabil


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IV.4. Regresii cu serii de

timp in Eviews


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Estimarea functiei de reactie Perioada analizata trim. I 1999 trim. I 2011

Serii de date utilizate: r_eu rata de politic monetar a BCE;

infl_eu inflaiei, msurat prin indicelearmonizat al preurilor, in Uniunea Monetar;

gap_eu output-gap-ul, calculat pe baza unuifiltru Hodrick-Prescott pentru zona euro;

dummy variabil dummy pentru perioada decriza financiara (ia valoarea 1 incepand cu trim. I2009)


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Parametrii regresiei


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Ecuatia estimata


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Indicatori ai regresiei

t-Statistic si probabilitatea asociata,calculat pentru constanta si coeficientul

fiecarei variabile independente

R-Squared, Adjusted R-Squared F-Statistic si probabilitatea asociata

Criteriile informationale (Akaike info

criterion, Schwarz criterion, Hannan-Quinncriter.)

Durbin-Watson stat


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Variabila dependenta evectiva

vs estimata

-.015

-.010

-.005

.000

.005

.010

.015

.00

.01

.02

.03

.04

.05

99 00 01 02 03 04 05 06 07 08 09 10 11

Residual Actual Fitted


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Teste asupra termenilor de eroare

Corelograma erorilor

Corelograma erorilor patratice

Testarea tipului de distributie a erorilor

Serial Correlation LM Test

ARCH LM Test

White Heteroskedasticity Test


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Selectare teste termeni de eroare


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T t di t ib ti i l


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Testarea distributiei normale a

erorilor regresiei

0

2

4

6

8

10

12

-0.010 -0.005 0.000 0.005 0.010 0.015

Series: ResidualsSample 1999Q1 2011Q1Observations 49

Mean -6.09e-18Median -0.000688Maximum 0.013773Minimum -0.010947Std. Dev. 0.005747Skewness 0.694016Kurtosis 2.892419

Jarque-Bera 3.957170Probability 0.138265


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Testarea corelatiei seriale


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Testarea termenilor ARCH


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Teste de stabilitate

CUSUM Test

CUSUM of Squares Test

Recursive Coeficients


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Teste de stabilitate


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CUSUM Test

-25

-20

-15

-10

-5

0

5

10

II III IV I II III IV I

2009 2010 2011

CUSUM 5% Significance


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CUSUM of Squares Test

-0.4

0.0

0.4

0.8

1.2

1.6


2009 2010 2011

CUSUM of Squares 5% Significance


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Recursive coeficients

.027

.028

.029

.030

.031

.032

.033

.034


2009 2010 2011

Recursive C(1) Estimates

2 S.E.

-.8

-.6

-.4

-.2

.0

.2

.4


2009 2010 2011


2 S.E.

.3

.4

.5

.6

.7

.8


2009 2010 2011


2 S.E.

-.020

-.015

-.010

-.005

.000

.005

.010


2009 2010 2011


2 S.E.


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V. Modele ARMA


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Modele ARMA

Modele autoregresive (AR);

Modele cu medii mobile (MA);

ModeleARMA care combina cele doutipuri de procese.


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Estimare modele ARMA

1. Testarea stationaritatii seriei2. Stationarizarea seriei

3. Pe baza coeficienilor de autocorelaie

(funciei de autocorelaie) i a coeficienilorde corelaie parial (funciei de autocorelaie

parial) se determin modelele

autoregresive de start pentru analiza serieide date.


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Estimare modele ARMA

4. Se estimeaza parametri modelelorARMA.

5. Se testeaza caracteristicile modelelor

autoregresive ce au fost estimate n etapaanterioara.

6. Se alege cel mai potrivit model folosind

diverse criterii de analiza.7. Pe baza modelului selectat se fac

diverse analize si prognoze


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V.4. Estimarea modelelor

ARMA in Eviews


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Seria de date

0

50

100

150

200

250

97 98 99 00 01 02 03 04 05 06 07

BUBOR


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Testul de stationaritate ADF

Null Hypothesis: BUBOR has a unit root


Lag Length: 0 (Automatic based on SIC, MAXLAG=12)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -5.024900 0.0003


5% level -3.445590

10% level -3.147710

*MacKinnon (1996) one-sided p-values.

Testul de stationaritate Philips


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Testul de stationaritate Philips-

PerronNull Hypothesis: BUBOR has a unit root


Bandwidth: 3 (Newey-West using Bartlett kernel)

Adj. t-Stat Prob.*

Phillips-Perron test statistic -5.437216 0.0001


5% level -3.445590

10% level -3.147710

*MacKinnon (1996) one-sided p-values.

Residual variance (no correction) 364.8682

HAC corrected variance (Bartlett kernel) 462.5140

F ti d t l ti


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S ifi ti


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Specificare ecuatie


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Estimare model MA(4)Dependent Variable: BUBOR

Method: Least Squares

Sample (adjusted): 1997M01 2007M08

Included observations: 128 after adjustments

Convergence achieved after 15 iterations

Backcast: 1996M09 1996M12

Variable Coefficient Std. Error t-Statistic Prob.

C 41.54023 5.901126 7.039374 0.0000

MA(1) 0.734234 0.051566 14.23862 0.0000

MA(2) 0.495279 0.026993 18.34853 0.0000

MA(3) 0.863535 0.025672 33.63763 0.0000

MA(4) 0.804961 0.050194 16.03709 0.0000

R-squared 0.838087 Mean dependent var 43.94414

Adjusted R-squared 0.832822 S.D. dependent var 42.18206S.E. of regression 17.24715 Akaike info criterion 8.571450

Sum squared resid 36588.11 Schwarz criterion 8.682858

Log likelihood -543.5728 F-statistic 159.1672

Durbin-Watson stat 1.582016 Prob(F-statistic) 0.000000

Inverted MA Roots .42-.90i .42+.90i -.78+.45i -.78-.45i


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Analiza radacini ecuatie

R d i il li l i t i ti


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Radacinile polinomului caracteristic

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

MA roots

Inverse Roots of AR/MA Polynomial(s)

Inverse Roots of AR/MA Polynomial(s)

Specification: BUBOR C MA(1) MA(2) MA(3) MA(4)

Sample: 1997M01 2007M12

Included observations: 128

MA Root(s) Modulus Cycle

0.416806 0.900818i 0.992572 5.524002

-0.783923 0.450021i 0.903910 2.397739

No root lies outside the unit circle.

ARMA model is invertible.

C


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V l f i i


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Valoarea efectiva vs estimata

-80

-40

0

40

80

0

50

100

150

200

250

97 98 99 00 01 02 03 04 05 06 07


E ti d l AR(1)


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Estimare model AR(1)Dependent Variable: BUBOR

Method: Least Squares




C 4.985180 2.639138 1.888943 0.0612

BUBOR(-1) 0.878633 0.043240 20.32007 0.0000




Log likelihood -562.7322 F-statistic 412.9052


C l il


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V l f ti ti t


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Valoarea efectiva vs estimata

-100

-50

0

50

100

150

0

50

100

150

200

250

97 98 99 00 01 02 03 04 05 06 07



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Estimare model ARMA(1,10)Dependent Variable: BUBOR

Method: Least SquaresSample (adjusted): 1997M02 2007M08



Backcast: 1996M04 1997M01


BUBOR(-1) 0.974210 0.017718 54.98466 0.0000

MA(5) -0.243541 0.056540 -4.307386 0.0000

MA(6) -0.226437 0.055472 -4.081987 0.0001

MA(7) -0.332302 0.055472 -5.990446 0.0000

MA(10) 0.476373 0.060775 7.838351 0.0000




Log likelihood -527.0577 Durbin-Watson stat 2.297258

Inverted MA Roots .88+.16i .88-.16i .56+.83i .56-.83i

-.02-.90i -.02+.90i -.53+.73i -.53-.73i

-.89+.33i -.89-.33i

C diti d t bilit t


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Conditia de stabilitate

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

MA roots

Inverse Roots of AR/MA Polynomial(s)Inverse Roots of AR/MA Polynomial(s)

Specification: BUBOR BUBOR(-1) MA(5) MA(6)

MA(7) MA(10)

Sample: 1997M01 2007M12


MA Root(s) Modulus Cycle

0.558806 0.826275i 0.997494 6.436651

-0.890402 0.332511i 0.950463 2.256737

-0.528267 0.734115i 0.904428 2.863081

-0.022438 0.897521i 0.897802 3.937348

0.882301 0.159193i 0.896548 35.19821

No root lies outside the unit circle.

ARMA model is invertible.


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Valori efective vs estimate


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Valori efective vs estimate

-80

-40

0

40

80

120

0

50

100

150

200

250

97 98 99 00 01 02 03 04 05 06 07


Selectarea specificatiei


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Selectarea specificatiei

MA(4) AR(1) ARMA(1,10)

Adjusted R-squared 0.832822 0.765758 0.863156

Akaike info criterion8.571450 8.893420 8.378862

Schwarz criterion8.682858 8.938210 8.490837


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Prognoze

Dynamic forecast prognozeaza valoarea

in perioada t + 1pe baza datelor efective

pana an momentul t, apoi pentru toateperioadele urmatoare foloseste datele deja

prognozate incepand din momentul t + 1.

Static forecast prognozeaza o observatieinainte numai pe baza datelor efective.


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Realizarea de prognoze

Prognoza dinamica a seriei


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Prognoza dinamica a seriei

-60

-40

-20

0

20

40

60

80

2007M09 2007M10 2007M11 2007M12

BUBORF


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VI. Modele cu date panel

Modele cu date panel


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Modele cu date panel

Constau in estimarea de ecuatii de

regresie in care sunt folosite date care sunt

in acelasi timp atat serii de timp ct si datecrosssectionale

Utilizari


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Utilizari

Rezumarea printr-un singur coeficient al impactului unei

variabile asupra unui grup de serii de timp variabile

dependente (grup de companii, de tari, etc.).

Estimarea de coeficienti specifici (constanta sau

coeficienti ai variabilelor independente) pentru fiecareserie de timp considerata ca variabila dependenta

efecte fixe.

Gruparea variabilelor dependente in categorii si estimarea

impactului categoriei din care face parte variabiladependenta asupra evolutiei acesteia

D fi i d l l i


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Definirea modelului


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Definirea indentificatorilor


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Definirea seriilor

E ti d i


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Ecuatia de regresie

Rezultate regresie


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Rezultate regresieDependent Variable: DLOG(HICP?)

Method: Pooled EGLS (Cross-section SUR)


Cross-sections included: 4

Total pool (balanced) observations: 752

Linear estimation after one-step weighting matrix


C 0.000698 0.000445 1.566998 0.1175

DLOG(HICP_EU(-1)) 0.612692 0.104768 5.848058 0.0000DLOG(HICP?(-1)) 0.553629 0.030088 18.40025 0.0000

DLOG(ER?(-1)) 0.083851 0.012757 6.572889 0.0000

Weighted Statistics


Adjusted R-squared 0.445443 S.D. dependent var 1.207505

S.E. of regression 0.928331 Sum squared resid 644.6258

F-statistic 202.0780 Durbin-Watson stat 2.104933Prob(F-statistic) 0.000000

Unweighted Statistics


Sum squared resid 0.080251 Durbin-Watson stat 1.864487

Coeficienti indi id ali


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Coeficienti individuali

Rezultate regresie


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Included observations: 188 after adjustmentsCross-sections included: 4




C 0.002113 0.000471 4.489158 0.0000

DLOG(HICP_EU(-1)) 0.631560 0.102724 6.148098 0.0000

DLOG(HICP?(-1)) 0.492847 0.031776 15.50997 0.0000

DLOG(ER?(-1)) 0.077977 0.012530 6.223189 0.0000

Fixed Effects (Cross)

_CZ--C -0.002185

_HU--C -0.000839

_PO--C -0.001681

_RO--C 0.004706

Effects Specification

Cross-section fixed (dummy variables)

Weighted Statistics


Adjusted R-squared 0.461768 S.D. dependent var 1.221242


F-statistic 108.3850 Durbin-Watson stat 2.054515

Prob(F-statistic) 0.000000




Impactul anticipatiilor inflationiste


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Impactul anticipatiilor inflationiste

Rezultate regresie


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Included observations: 188 af ter adjustmentsCross-sections included: 4




C 0.001447 0.000443 3.264956 0.0011

DLOG(HICP_EU(-1)) 0.572149 0.102100 5.603786 0.0000

DLOG(ER?(-1)) 0.065592 0.012463 5.262752 0.0000

_CZ--DLOG(HICP_CZ(-1)) 0.193372 0.066868 2.891863 0.0039

_HU--DLOG(HICP_HU(-1)) 0.406401 0.052893 7.683466 0.0000

_PO--DLOG(HICP_PO(-1)) 0.326507 0.063476 5.143756 0.0000

_RO--DLOG(HICP_RO(-1)) 0.686025 0.035300 19.43402 0.0000

Weighted Statistics


Adjusted R-squared

0.468508

S.D. dependent var

1.220327







Impactul cursului de schimb


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Impactul cursului de schimb

Rezultate regresie


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Included observations: 188 af ter adjustmentsCross-sections included: 4




C 0.001175 0.000383 3.064805 0.0023

DLOG(HICP_EU(-1)) 0.513687 0.090404 5.682137 0.0000

DLOG(HICP?(-1)) 0.405206 0.028875 14.03333 0.0000

_CZ--DLOG(ER_CZ(-1)) 0.053506 0.026337 2.031585 0.0426

_HU--DLOG(ER_HU(-1)) 0.006168 0.017179 0.359047 0.7197

_PO--DLOG(ER_PO(-1)) 0.020524 0.011008 1.864565 0.0626

_RO--DLOG(ER_RO(-1)) 0.417841 0.030630 13.64161 0.0000

Weighted Statistics


Adjusted R-squared

0.502068

S.D. dependent var

1.354914








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VII. Modele GARCH

Ti i d l tilit t


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Tipuri de volatilitate

Istorica calculata pe baza preturiloristorice ale activelor

Exponentialy weighted moving average -

EWMA Estimata prin modele econometrice

(Generalised Autoregressive Conditional

Heteroskedasticity - GARCH) Implicita calculata din preturile optiunilor

Calcul volatilitate istorica


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Calcul volatilitate istorica

1. Observatii curs spot S0, S1, . . . , Sn laintervale de ani

2. Calcul randament in timp continuu:

3. Calculul deviatiei standard, s,pentru randamentele ui

4. Estimarea volatilitatii istorice ca:

u

S

Sii

i=

ln

1

=

s

Modelul EWMA


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Modelul EWMA

Conform acestui model, volatilitatea dinziua neste o medie ponderata intre

volatilitatea din ziua anterioara si

randamentul la patrat u2

din ziuaanterioara

RiskMetrics (JP Morgan, Reuters)foloseste = 0.94 pentru calculul

volatilitatii zilnice

2

1

2

1

2)1( += nnn u

Modele GARCH


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Modele GARCH

In modelul GARCH, volatilitatea depindede volatilitatile anterioare si de

randamentele patratice anterioare ale

activului

Coeficientii variabielor sunt extimati prin

diverse proceduri econometrice

2

1

2

1

2in

q

i

ikn

p

k

kn u =

= ++=

Tipuri de modele GARCH


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Tipuri de modele GARCH

ARCH

GARCH

GARCH in Mean

Treshold ARCH - TARCH

Exponential GARCH - EGARCH

Integrated GARCH - IGARCH

Specificare model


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Specificare model


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Estimare GARCH(1 1)


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Estimare GARCH(1,1)Dependent Variable: DL_EUR

Method: ML - ARCH (Marquardt) - Normal distribution

Sample (adjusted): 2 2148Included observations: 2147 after adjustments


Variance backcast: ON

GARCH = C(2) + C(3)*RESID(-1)^2 + C(4)*GARCH(-1)

Coefficient Std. Error z-Statistic Prob.

C 0.000198 8.77E-05 2.260467 0.0238

Variance Equation

C 2.50E-07 5.08E-08 4.926018 0.0000

RESID(-1)^2 0.138819 0.009128 15.20872 0.0000

GARCH(-1)

0.868095

0.008286

104.7609

0.0000

R-squared -0.001355 Mean dependent var 0.000427

Adjusted R-squared -0.002757 S.D. dependent var 0.006208

S.E. of regression 0.006216 Akaike info criterion -7.718359

Sum squared resid 0.082811 Schwarz criterion -7.707792

Log likelihood 8289.659 Durbin-Watson stat 1.848831

Estimare EGARCH(2,1,1)


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Estimare EGARCH(2,1,1)Dependent Variable: DL_EUR

Method: ML - ARCH (Marquardt) - Generalized error distribution (GED)

Sample (adjusted): 2 2148



Variance backcast: ON

LOG(GARCH) = C(3) + C(4)*ABS(RESID(-1)/@SQRT(GARCH(-1))) +

C(5)*ABS(RESID(-2)/@SQRT(GARCH(-2))) + C(6)*RESID(-1)

/@SQRT(GARCH(-1)) + C(7)*LOG(GARCH(-1))

Coefficient Std. Error z-Statistic Prob.

@SQRT(GARCH) 0.112635 0.039554 2.847620 0.0044

C -0.000457 0.000156 -2.932430 0.0034

Variance Equation

C(3) -0.284286 0.056336 -5.046247 0.0000

C(4) 0.399824 0.049811 8.026844 0.0000

C(5) -0.170567 0.049394 -3.453202 0.0006

C(6) -0.026267 0.013602 -1.931131 0.0535

C(7) 0.989348 0.004282 231.0737 0.0000

GED PARAMETER 1.293394 0.047198 27.40373 0.0000


Adjusted R-squared -0.001266 S.D. dependent var 0.006208

S.E. of regression 0.006212 Akaike info criterion -7.788111

Sum squared resid 0.082534 Schwarz criterion -7.766977

Log likelihood 8368.537 F-statistic 0.612409




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V l tilit t diti t


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Volatilitatea conditionata

.000

.004

.008

.012

.016

.020

.024

.028

250 500 750 1000 1250 1500 1750 2000

Conditional standard deviation


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VIII. Modele cu vectori

autoregresivi (VAR)

Definitie si utilizare


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Definitie si utilizare

Un model VAR(Vector Autoregression) permite

tratarea simetrica a tuturor variabilelor din model,

in sensul ca nu presupune implicit exogeneitatea

unei anumite variabile (cum se intampla in cazul

OLS).

Construire model VAR


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Construire model VAR

Alegere numar de lag-uri


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ege e u a de ag u

Alegere numar lag-uri


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Alegere numar lag uri

Stabilitate model VAR


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Stabilitate model VAR

Stationaritate model VAR


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-.6

-.4

-.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 10 11 12

Cor(DLOG(HICP_RO),DLOG(HICP_RO)(-i))

-.6

-.4

-.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 10 11 12

Cor(DLOG(HICP_RO),DLOG(ER_RO)(-i))

-.6

-.4

-.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 10 11 12

Cor(DLOG(HICP_RO),DLOG(HICP_EU)(-i))

-.6

-.4

-.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 10 11 12

Cor(DLOG(ER_RO),DLOG(HICP_RO)(-i))

-.6

-.4

-.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 10 11 12

Cor(DLOG(ER_RO),DLOG(ER_RO)(-i))

-.6

-.4

-.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 10 11 12

Cor(DLOG(ER_RO),DLOG(HICP_EU)(-i))

-.6

-.4

-.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 10 11 12

Cor(DLOG(HICP_EU),DLOG(HICP_RO)(-i))

-.6

-.4

-.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 10 11 12

Cor(DLOG(HICP_EU),DLOG(ER_RO)(-i))

-.6

-.4

-.2

.0

.2

.4

.6

1 2 3 4 5 6 7 8 9 10 11 12

Cor(DLOG(HICP_EU),DLOG(HICP_EU)(-i))

Autocorrelations with 2 Std.Err. Bounds

Testarea autocorelatiei


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VAR Residual Portmanteau Tests for Autocorrelations

Null Hypothesis: no residual autocorrelations up to lag hSample: 1996M01 2011M12


Lags Q-Stat Prob. Adj Q-Stat Prob. df

1 0.497749 NA* 0.500439 NA* NA*

2 1.487910 NA* 1.501363 NA* NA*

3 4.163052 NA* 4.220360 NA* NA*

4 22.25030 0.1353 22.70513 0.1218 16

5 35.55546 0.0786 36.37783 0.0661 25

6 52.90164 0.0204 54.30223 0.0150 34

7 64.09821 0.0201 65.93665 0.0138 43

8 81.99966 0.0050 84.64266 0.0028 52

9 89.82131 0.0096 92.86202 0.0053 61

10 95.09797 0.0247 98.43849 0.0141 7011 99.91440 0.0561 103.5577 0.0334 79

12 154.0077 0.0000 161.3815 0.0000 88

*The test is valid only for lags larger than the VAR lag order.

df is degrees of freedom for (approximate) chi-square distribution

Testarea autocorelatiei


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VAR Residual Serial Correlation LM Tests

Null Hypothesis: no serial correlation at lag order hSample: 1996M01 2011M12


Lags LM-Stat Prob

1 9.676269 0.3773

2 6.781290 0.6599

3 17.34069 0.0436

4 21.62957 0.0101

5 14.02825 0.1213

6 18.97320 0.0254

7 12.64418 0.1794

8 20.40055 0.01569 8.294159 0.5048

10 5.512769 0.7875

11 5.240046 0.8129

12 72.10294 0.0000

Probs from chi-square with 9 df.

Testarea distributiei normale


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VAR Residual Normality Tests

Orthogonalization: Cholesky (Lutkepohl)

Null Hypothesis: residuals are multivariate normal

Sample: 1996M01 2011M12


Component Skewness Chi-sq df Prob.

1 1.088627 36.73835 1 0.0000

2 0.763380 18.06523 1 0.0000

3 -0.043528 0.058734 1 0.8085

Joint 54.86231 3 0.0000

Component Kurtosis Chi-sq df Prob.

1 5.840031 62.50978 1 0.0000

2 12.63516 719.4818 1 0.0000

3 4.804536 25.23672 1 0.0000

Joint 807.2283 3 0.0000

Component Jarque-Bera df Prob.

1 99.24813 2 0.0000

2 737.5470 2 0.0000

3 25.29545 2 0.0000

Joint 862.0906 6 0.0000

Testarea heteroskedasticitatii


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VAR Residual Heteroskedasticity Tests: No Cross Terms (only levels and squares)

Sample: 1996M01 2011M12


Joint test:

Chi-sq df Prob.

420.2497 108 0.0000

Individual components:

Dependent R-squared F(18,167) Prob. Chi-sq(18) Prob.

res1*res1 0.359985 5.218402 0.0000 66.95714 0.0000

res2*res2 0.458122 7.843734 0.0000 85.21061 0.0000

res3*res3 0.410657 6.464790 0.0000 76.38214 0.0000

res2*res1 0.414220 6.560566 0.0000 77.04500 0.0000

res3*res1 0.137523 1.479350 0.1029 25.57924 0.1098

res3*res2 0.715462 23.32867 0.0000 133.0759 0.0000

Definitia impulsului


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p Definitia impulsurilor conteaza deoarece:

in cazul descompunerii Cholesky conteaza

ordonarea variabilelor daca acestea sunt

corelate intre ele;

in cazul descompunerii generalizate nuconteaza ordonarea variabilelor;

in cazul descompunerii structurale, aceasta

poate fi utilizata doar daca a fost specificat

anterior un model structural cu restrictiile

necesare.

Functii de impuls-raspuns


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Functii de impuls-raspuns


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p p

-.010

-.005

.000

.005

.010

.015

.020

1 2 3 4 5 6 7 8 9 10 11 12

Response of DLOG(HICP_RO) to DLOG(HICP_RO)

-.010

-.005

.000

.005

.010

.015

.020

1 2 3 4 5 6 7 8 9 10 11 12

Response of DLOG(HICP_RO) to DLOG(ER_RO)

-.010

-.005

.000

.005

.010

.015

.020

1 2 3 4 5 6 7 8 9 10 11 12

Response of DLOG(HICP_RO) to DLOG(HICP_EU)

Response to Cholesky One S.D. Innovations 2 S.E.

-.02

-.01

.00

.01

.02

.03

.04

1 2 3 4 5 6 7 8 9 10 11 12

Response of DLOG(ER_RO) to DLOG(HICP_RO)

-.02

-.01

.00

.01

.02

.03

.04

1 2 3 4 5 6 7 8 9 10 11 12

Response of DLOG(ER_RO) to DLOG(ER_RO)

-.02

-.01

.00

.01

.02

.03

.04

1 2 3 4 5 6 7 8 9 10 11 12

Response of DLOG(ER_RO) to DLOG(HICP_EU)

Response to Cholesky One S.D. Innovations 2 S.E.

Descompunerea variantei


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0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12

Percent DLOG(HICP_RO) variance due to DLOG(HICP_RO)

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12

Percent DLOG(HICP_RO) variance due to DLOG(ER_RO)

80

100Percent DLOG(HICP_RO) variance due to DLOG(HICP_EU)

Variance Decomposition

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12

Percent DLOG(ER_RO) variance due to DLOG(HICP_RO)

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12

Percent DLOG(ER_RO) variance due to DLOG(ER_RO)

80

100Percent DLOG(ER_RO) variance due to DLOG(HICP_EU)

Variance Decomposition

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