Applied Macro and Financial
Econometrics
Multivariate Time Series
Cointegration
Course Coordinator:
Dr. Devasmita Jena
Cointegration
Definition: A set of time series variables are cointegrated if a linear combination of them is
stationary
Regressing two non stationary variables doesn't amount to spurious regression if the variables
are cointegrated
Many times series variables are non stationary, but “move together” over time
The series are bound by some relationship in the long term
Cointegrating relationship => long-term or equilibrium phenomenon
It is possible that cointegrating variables deviate from their relationship in the short run, but
their association would return in the long run
Equilibrium correction/Error Correction Models
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Testing for Cointegration
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Parameter estimation in cointegrated systems
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Engle-Yoo 3-step Method
Drawback of Engle-Granger 2-step Method:
1. finite sample problem -> lack of power in unit root test and cointegration
2. simultaneous equations bias
3. not possible to perform any hypothesis tests about the actual cointegrating relationship estimated at stage 1
4. only one cointegrating relationship can be identified
Problems 1 and 2 are small sample problems that should disappear asymptotically
Problem 3 is addressed by Engle-Yoo and Johansen methods
Engle-Yoo Method:
• First two steps are exactly same as the Engle--Granger method
• In the third step Engle and Yoo gives updated estimates of the cointegrating vector and its standard errors
• The Engle and Yoo (EY) third step is algebraically technical
• The Engle Yoo method suffers from all of the remaining problems of the EG approach
Johansen Cointegration Method
•1
Johansen Cointegration Test
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Johansen Cointegration: Hypothesis Testing
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Johansen Cointegration Test (contd…)
The Johansen Test is conducted sequentially:
• H0: r=0 against H1: 0<r ≤g
• H0: r=1 against H1: 1<r ≤g
• and likewise till
• H0: r=g-1 against H1: r=g
That is, value of r is continually increased until the H0 is no longer rejected
