Lecture: Introduction to CointegrationApplied Econometrics

Jozef Barunik

IES, FSV, UK

Summer Semester 2010/2011

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 1 / 18

Introduction Readings

Readings

1 The Royal Swedish Academy of Sciences (2003): Time SeriesEconometrics: Cointegration and Autoregressive ConditionalHeteroscedasticity, downloadable from:http://www-stat.wharton.upenn.edu/∼steele/HoldingPen/NobelPrizeInfo.pdf

2 Granger,C.W.J. (2003): Time Series, Cointegration and Applications,Nobel lecture, December 8, 2003

3 Harris Using Cointegration Analysis in Econometric Modelling, 1995

(Useful applied econometrics textbook focused solely on cointegration)

4 Almost all textbooks cover the introduction to cointegration

Engle-Granger procedure (single equation procedure),

Johansen multivariate framework (covered in the following lecture)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 2 / 18

Introduction Outline

Outline of the today’s talk

What is cointegration?

Deriving Error-Correction Model (ECM)

Engle-Granger procedure

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 3 / 18

Introduction Outline

Outline of the today’s talk

What is cointegration?

Deriving Error-Correction Model (ECM)

Engle-Granger procedure

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 3 / 18

Introduction Outline

Outline of the today’s talk

What is cointegration?

Deriving Error-Correction Model (ECM)

Engle-Granger procedure

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 3 / 18

Introduction Outline

Robert F. Engle and Clive W.J. Granger

Robert F. Engle shared the Nobel prize (2003) “for methods of analyzingeconomic time series with time-varying volatility (ARCH) with Clive W. J.Granger who recieved the prize “for methods of analyzing economic timeseries with common trends (cointegration).

Figure: (a) Robert F. Engle (b) Clive W.J. Granger

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 4 / 18

Introduction Introduction

Introduction

We learnt that regressing two non-stationary variables (say Yt on Xt)results in spurious regression

However, if Yt and Xt are cointegrated, spurious regression no longerarise

Success of large structural macro models in the 1960s due to trendvs. its failure in 1970s

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 5 / 18

Introduction Introduction

Introduction

We learnt that regressing two non-stationary variables (say Yt on Xt)results in spurious regression

However, if Yt and Xt are cointegrated, spurious regression no longerarise

Success of large structural macro models in the 1960s due to trendvs. its failure in 1970s

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 5 / 18

Introduction Introduction

Introduction

We learnt that regressing two non-stationary variables (say Yt on Xt)results in spurious regression

However, if Yt and Xt are cointegrated, spurious regression no longerarise

Success of large structural macro models in the 1960s due to trendvs. its failure in 1970s

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 5 / 18

Introduction Introduction

Introduction cont.

Assume two time series Yt , and Xt , are integrated of orderd(Yt ,Xt ∼ I (d))

If there exists β such that Yt − β ∗ Xt = ut , where ut is integrated oforder less than d (say d − b), we say that Yt and Xt are cointegratedof order d − b, Yt , Xt ∼ CI (d , b)

For example, money supply and price level are typically integrated oforder one (Yt ,Xt ∼ I (1)), but their difference should be stationary(I (0)) in the long run, as money supply and price level cannotaccording to economic theory diverge in the long run.

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 6 / 18

Introduction Introduction

Introduction cont.

Assume two time series Yt , and Xt , are integrated of orderd(Yt ,Xt ∼ I (d))

If there exists β such that Yt − β ∗ Xt = ut , where ut is integrated oforder less than d (say d − b), we say that Yt and Xt are cointegratedof order d − b, Yt , Xt ∼ CI (d , b)

For example, money supply and price level are typically integrated oforder one (Yt ,Xt ∼ I (1)), but their difference should be stationary(I (0)) in the long run, as money supply and price level cannotaccording to economic theory diverge in the long run.

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 6 / 18

Introduction Introduction

Introduction cont.

Assume two time series Yt , and Xt , are integrated of orderd(Yt ,Xt ∼ I (d))

If there exists β such that Yt − β ∗ Xt = ut , where ut is integrated oforder less than d (say d − b), we say that Yt and Xt are cointegratedof order d − b, Yt , Xt ∼ CI (d , b)

For example, money supply and price level are typically integrated oforder one (Yt ,Xt ∼ I (1)), but their difference should be stationary(I (0)) in the long run, as money supply and price level cannotaccording to economic theory diverge in the long run.

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 6 / 18

Introduction Introduction

Introduction cont.

The prices of goods expressed in common currency should be identical, soSt ∗ Pt,foreign = Pt

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 7 / 18

Introduction Introduction

Introduction cont.

If St ,Pt,foreign and Pt are I (1) and cointegrated, its linear combination isI (0).

Figure: Regression residuals

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 8 / 18

Introduction Introduction

Introduction cont.

If Yt and Xt are integrated of order one and are cointegrated, you donot have to difference the data and may (simply by OLS) estimateYt = ρ+ β ∗ Xt + ut

β is superconsistent in this case, converge to its true counterpart at afaster rate than the usual OLS estimator with I (0) variables ∆Yt and∆Xt , however standard errors not consistent, not worth reporting

Note that, if you want to difference Yt and Xt , you will not have unitroot in variables Yt and Xt but unit root will arise in the error termut = et − et−1 (overdifferenced data)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 9 / 18

Introduction Introduction

Introduction cont.

If Yt and Xt are integrated of order one and are cointegrated, you donot have to difference the data and may (simply by OLS) estimateYt = ρ+ β ∗ Xt + ut

β is superconsistent in this case, converge to its true counterpart at afaster rate than the usual OLS estimator with I (0) variables ∆Yt and∆Xt , however standard errors not consistent, not worth reporting

Note that, if you want to difference Yt and Xt , you will not have unitroot in variables Yt and Xt but unit root will arise in the error termut = et − et−1 (overdifferenced data)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 9 / 18

Introduction Introduction

Introduction cont.

If Yt and Xt are integrated of order one and are cointegrated, you donot have to difference the data and may (simply by OLS) estimateYt = ρ+ β ∗ Xt + ut

β is superconsistent in this case, converge to its true counterpart at afaster rate than the usual OLS estimator with I (0) variables ∆Yt and∆Xt , however standard errors not consistent, not worth reporting

Note that, if you want to difference Yt and Xt , you will not have unitroot in variables Yt and Xt but unit root will arise in the error termut = et − et−1 (overdifferenced data)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 9 / 18

Introduction Introduction

Introduction cont.

Note

If say X ∼ I (0) and Y ∼ I (1), surely no cointegration (no long runrelationship), X is more or less constant over time, while Y increases overtime

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 10 / 18

Cointegration Cointegration

Cointegration

If you difference I(1) data, you lose long run information and estimateonly short run model

This is, with differenced data you know what is the effect of the change of x on

change of y , not the level effect

Alternative is to use error-correction model (ECM), great advantageis that you may model both short run and long run relationship jointly(if variables cointegrated)

Granger representation theorem: for any set of I(1) variables, errorcorrection and cointegration are the equivalent representations(‘same’)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 11 / 18

Cointegration Cointegration

Cointegration

If you difference I(1) data, you lose long run information and estimateonly short run model

This is, with differenced data you know what is the effect of the change of x on

change of y , not the level effect

Alternative is to use error-correction model (ECM), great advantageis that you may model both short run and long run relationship jointly(if variables cointegrated)

Granger representation theorem: for any set of I(1) variables, errorcorrection and cointegration are the equivalent representations(‘same’)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 11 / 18

Cointegration Cointegration

Cointegration

If you difference I(1) data, you lose long run information and estimateonly short run model

This is, with differenced data you know what is the effect of the change of x on

change of y , not the level effect

Alternative is to use error-correction model (ECM), great advantageis that you may model both short run and long run relationship jointly(if variables cointegrated)

Granger representation theorem: for any set of I(1) variables, errorcorrection and cointegration are the equivalent representations(‘same’)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 11 / 18

Cointegration Deriving ECM

Deriving ECM

Assume the model Ct = α0 + α1Ct−1 + β0Yt + β1Yt−1 + ut andassume Ct and Yt both ∼ I (1)

Subtract Ct−1 from both sides of equation and get

∆Ct = α0 + ρ1Ct−1 + β0Yt + β1Yt−1 + ut (1)

Now add: −β0Yt−1 + β0Yt−1 and get:

∆Ct = α0 + ρ1Ct−1 + β0∆Yt + θ1Yt−1 + ut (2)

Now, LHS stationary, ∆Yt stationary, if Ct and Yt cointegrated (thustogether I(0)), then ut must be I(0) as well

May generalize to more variables and time trend as well

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 12 / 18

Cointegration Deriving ECM

Deriving ECM

Assume the model Ct = α0 + α1Ct−1 + β0Yt + β1Yt−1 + ut andassume Ct and Yt both ∼ I (1)

Subtract Ct−1 from both sides of equation and get

∆Ct = α0 + ρ1Ct−1 + β0Yt + β1Yt−1 + ut (1)

Now add: −β0Yt−1 + β0Yt−1 and get:

∆Ct = α0 + ρ1Ct−1 + β0∆Yt + θ1Yt−1 + ut (2)

Now, LHS stationary, ∆Yt stationary, if Ct and Yt cointegrated (thustogether I(0)), then ut must be I(0) as well

May generalize to more variables and time trend as well

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 12 / 18

Cointegration Deriving ECM

Deriving ECM

Assume the model Ct = α0 + α1Ct−1 + β0Yt + β1Yt−1 + ut andassume Ct and Yt both ∼ I (1)

Subtract Ct−1 from both sides of equation and get

∆Ct = α0 + ρ1Ct−1 + β0Yt + β1Yt−1 + ut (1)

Now add: −β0Yt−1 + β0Yt−1 and get:

∆Ct = α0 + ρ1Ct−1 + β0∆Yt + θ1Yt−1 + ut (2)

Now, LHS stationary, ∆Yt stationary, if Ct and Yt cointegrated (thustogether I(0)), then ut must be I(0) as well

May generalize to more variables and time trend as well

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 12 / 18

Cointegration Deriving ECM

Deriving ECM

Assume the model Ct = α0 + α1Ct−1 + β0Yt + β1Yt−1 + ut andassume Ct and Yt both ∼ I (1)

Subtract Ct−1 from both sides of equation and get

∆Ct = α0 + ρ1Ct−1 + β0Yt + β1Yt−1 + ut (1)

Now add: −β0Yt−1 + β0Yt−1 and get:

∆Ct = α0 + ρ1Ct−1 + β0∆Yt + θ1Yt−1 + ut (2)

Now, LHS stationary, ∆Yt stationary, if Ct and Yt cointegrated (thustogether I(0)), then ut must be I(0) as well

May generalize to more variables and time trend as well

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 12 / 18

Cointegration Deriving ECM

Deriving ECM

Assume the model Ct = α0 + α1Ct−1 + β0Yt + β1Yt−1 + ut andassume Ct and Yt both ∼ I (1)

Subtract Ct−1 from both sides of equation and get

∆Ct = α0 + ρ1Ct−1 + β0Yt + β1Yt−1 + ut (1)

Now add: −β0Yt−1 + β0Yt−1 and get:

∆Ct = α0 + ρ1Ct−1 + β0∆Yt + θ1Yt−1 + ut (2)

Now, LHS stationary, ∆Yt stationary, if Ct and Yt cointegrated (thustogether I(0)), then ut must be I(0) as well

May generalize to more variables and time trend as well

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 12 / 18

Cointegration Testing for Cointegration

Testing for Cointegration

Test the residuals for a unit root (ADF test)

No constant required (if constant already included in originalregression)

∆ut = βut−1 + δ1∆ut−1 + · · ·+ δn∆ut−n + νt (3)

Test H0 : β = 0

β = 0⇒ Unit root ⇒ non-stationary ⇒ Yt and Xt not cointegrated

β 6= 0⇒ No Unit root ⇒ stationary ⇒ Yt and Xt cointegrated

Note DF critical values for CI are not the same as for I, critical valuesfrom Engle and Yoo (1987)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 13 / 18

Cointegration Testing for Cointegration

Testing for Cointegration

Test the residuals for a unit root (ADF test)

No constant required (if constant already included in originalregression)

∆ut = βut−1 + δ1∆ut−1 + · · ·+ δn∆ut−n + νt (3)

Test H0 : β = 0

β = 0⇒ Unit root ⇒ non-stationary ⇒ Yt and Xt not cointegrated

β 6= 0⇒ No Unit root ⇒ stationary ⇒ Yt and Xt cointegrated

Note DF critical values for CI are not the same as for I, critical valuesfrom Engle and Yoo (1987)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 13 / 18

Cointegration Testing for Cointegration

Testing for Cointegration

Test the residuals for a unit root (ADF test)

No constant required (if constant already included in originalregression)

∆ut = βut−1 + δ1∆ut−1 + · · ·+ δn∆ut−n + νt (3)

Test H0 : β = 0

β = 0⇒ Unit root ⇒ non-stationary ⇒ Yt and Xt not cointegrated

β 6= 0⇒ No Unit root ⇒ stationary ⇒ Yt and Xt cointegrated

Note DF critical values for CI are not the same as for I, critical valuesfrom Engle and Yoo (1987)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 13 / 18

Cointegration Testing for Cointegration

Testing for Cointegration

Test the residuals for a unit root (ADF test)

No constant required (if constant already included in originalregression)

∆ut = βut−1 + δ1∆ut−1 + · · ·+ δn∆ut−n + νt (3)

Test H0 : β = 0

β = 0⇒ Unit root ⇒ non-stationary ⇒ Yt and Xt not cointegrated

β 6= 0⇒ No Unit root ⇒ stationary ⇒ Yt and Xt cointegrated

Note DF critical values for CI are not the same as for I, critical valuesfrom Engle and Yoo (1987)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 13 / 18

Cointegration Testing for Cointegration

Testing for Cointegration

Test the residuals for a unit root (ADF test)

No constant required (if constant already included in originalregression)

∆ut = βut−1 + δ1∆ut−1 + · · ·+ δn∆ut−n + νt (3)

Test H0 : β = 0

β = 0⇒ Unit root ⇒ non-stationary ⇒ Yt and Xt not cointegrated

β 6= 0⇒ No Unit root ⇒ stationary ⇒ Yt and Xt cointegrated

Note DF critical values for CI are not the same as for I, critical valuesfrom Engle and Yoo (1987)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 13 / 18

Cointegration Testing for Cointegration

Testing for Cointegration (cont.)

Alternatively, use Durbin-Watson (DW)

DW roughly equal to 2(1− ρ), where ρ is measure of autocorrelation

Null hypothesis: No CI, ρ = 1, DW=0

Alternative: CI, −1 < ρ < 1, DW>0

Developed by Sargan and Bhargava, 1983, but applicable only if theresidual follows 1-st order autoregression (not so widely used)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 14 / 18

Cointegration Testing for Cointegration

Testing for Cointegration (cont.)

Alternatively, use Durbin-Watson (DW)

DW roughly equal to 2(1− ρ), where ρ is measure of autocorrelation

Null hypothesis: No CI, ρ = 1, DW=0

Alternative: CI, −1 < ρ < 1, DW>0

Developed by Sargan and Bhargava, 1983, but applicable only if theresidual follows 1-st order autoregression (not so widely used)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 14 / 18

Cointegration Testing for Cointegration

Testing for Cointegration (cont.)

Alternatively, use Durbin-Watson (DW)

DW roughly equal to 2(1− ρ), where ρ is measure of autocorrelation

Null hypothesis: No CI, ρ = 1, DW=0

Alternative: CI, −1 < ρ < 1, DW>0

Developed by Sargan and Bhargava, 1983, but applicable only if theresidual follows 1-st order autoregression (not so widely used)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 14 / 18

Cointegration Testing for Cointegration

Testing for Cointegration (cont.)

Alternatively, use Durbin-Watson (DW)

DW roughly equal to 2(1− ρ), where ρ is measure of autocorrelation

Null hypothesis: No CI, ρ = 1, DW=0

Alternative: CI, −1 < ρ < 1, DW>0

Developed by Sargan and Bhargava, 1983, but applicable only if theresidual follows 1-st order autoregression (not so widely used)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 14 / 18

Cointegration Testing for Cointegration

Testing for Cointegration (cont.)

Alternatively, use Durbin-Watson (DW)

DW roughly equal to 2(1− ρ), where ρ is measure of autocorrelation

Null hypothesis: No CI, ρ = 1, DW=0

Alternative: CI, −1 < ρ < 1, DW>0

Developed by Sargan and Bhargava, 1983, but applicable only if theresidual follows 1-st order autoregression (not so widely used)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 14 / 18

Cointegration ECM Estimation

ECM Estimation

If you find evidence of cointegration, then specify the corresponding ECMEstimate the ECM using the lagged residuals (ut−1)

as the EC Mechanism∆Yt = β0 + β1∆Xt − β2(Yt−1 − C − βXt−1)

EC Mechanism

(Yt−1 − C − βXt−1) = ut−1 (4)

In the cointegrating regressionYt = C + βXt + ut

ut = Yt − C − βXt ⇒ ut−1 = Yt−1 − C − βXt−1 (5)

NOTE

(4) ≡ (5)⇒ ut−1 ≡ EC Mechanism

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 15 / 18

Cointegration Engle-Granger procedure

Engle-Granger procedure

1 Test the order of integration for all variables by unit root test such asADF or PP test

2 Estimate (by OLS) Ct = α0 + β0Yt + ut ,

3 Test for cointegration

4 Estimate error-correction model ∆Ct = α0 + β∆Yt + ρut−1 + et ,you may include lags of ∆Ct and ∆Yt in the RHS, if needed

NOTE

that ut−1 is from the equation in the step 2

5 Evaluate the model adequacy (note that the estimated parameter ρshould be negative and can be interpreted as the speed of adjustment)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 16 / 18

Cointegration Engle-Granger procedure

Engle-Granger procedure

1 Test the order of integration for all variables by unit root test such asADF or PP test

2 Estimate (by OLS) Ct = α0 + β0Yt + ut ,

3 Test for cointegration

4 Estimate error-correction model ∆Ct = α0 + β∆Yt + ρut−1 + et ,you may include lags of ∆Ct and ∆Yt in the RHS, if needed

NOTE

that ut−1 is from the equation in the step 2

5 Evaluate the model adequacy (note that the estimated parameter ρshould be negative and can be interpreted as the speed of adjustment)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 16 / 18

Cointegration Engle-Granger procedure

Engle-Granger procedure

1 Test the order of integration for all variables by unit root test such asADF or PP test

2 Estimate (by OLS) Ct = α0 + β0Yt + ut ,

3 Test for cointegration

4 Estimate error-correction model ∆Ct = α0 + β∆Yt + ρut−1 + et ,you may include lags of ∆Ct and ∆Yt in the RHS, if needed

NOTE

that ut−1 is from the equation in the step 2

5 Evaluate the model adequacy (note that the estimated parameter ρshould be negative and can be interpreted as the speed of adjustment)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 16 / 18

Cointegration Engle-Granger procedure

Engle-Granger procedure

1 Test the order of integration for all variables by unit root test such asADF or PP test

2 Estimate (by OLS) Ct = α0 + β0Yt + ut ,

3 Test for cointegration

4 Estimate error-correction model ∆Ct = α0 + β∆Yt + ρut−1 + et ,you may include lags of ∆Ct and ∆Yt in the RHS, if needed

NOTE

that ut−1 is from the equation in the step 2

5 Evaluate the model adequacy (note that the estimated parameter ρshould be negative and can be interpreted as the speed of adjustment)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 16 / 18

Cointegration Engle-Granger procedure

Engle-Granger procedure

1 Test the order of integration for all variables by unit root test such asADF or PP test

2 Estimate (by OLS) Ct = α0 + β0Yt + ut ,

3 Test for cointegration

4 Estimate error-correction model ∆Ct = α0 + β∆Yt + ρut−1 + et ,you may include lags of ∆Ct and ∆Yt in the RHS, if needed

NOTE

that ut−1 is from the equation in the step 2

5 Evaluate the model adequacy (note that the estimated parameter ρshould be negative and can be interpreted as the speed of adjustment)

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 16 / 18

Cointegration Drawback of Engle-Granger approach

Drawback of Engle-Granger approach

Single equation model

There can be more than one cointegrating relationships (if there aremore than 2 variables)

For example, 2 cointegration relationships likely for demand and supplyof credit

The drawback tackled by Johansen procedure

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 17 / 18

Cointegration Drawback of Engle-Granger approach

Drawback of Engle-Granger approach

Single equation model

There can be more than one cointegrating relationships (if there aremore than 2 variables)

For example, 2 cointegration relationships likely for demand and supplyof credit

The drawback tackled by Johansen procedure

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 17 / 18

Cointegration Drawback of Engle-Granger approach

Drawback of Engle-Granger approach

Single equation model

There can be more than one cointegrating relationships (if there aremore than 2 variables)

For example, 2 cointegration relationships likely for demand and supplyof credit

The drawback tackled by Johansen procedure

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 17 / 18

Cointegration Drawback of Engle-Granger approach

Questions

Thank you for your Attention !

Jozef Barunik (IES, FSV, UK) Lecture: Introduction to Cointegration Summer Semester 2010/2011 18 / 18