# Single equation regression models ppt

We can avoid this problem if long-run relationship is cointegrated Concept of cointegration introduced by Granger in 1981.Second section of lectures concerns relationships of this type.2Long-run Relationships Consider the following static **regression** between two variables Yt ß0 ß1Xt ut This relationship has the disequilibrium error ut (a linear combination of Yt and Xt) where ut Yt - ß0 - ß1Xt Engle and Granger (1987) if a long-run relationship exists, then the disequilibrium error should have a tendency to disappear.

However if there is a long-run relationship, errors have a tendency to disappear and return to zero i.e. If a linear combination of two I(1) variables generates I(0) errors, we say that the variables are cointegrated.

6Cointegration in **Single** **Equations** Definition Two time series are said to be cointegrated of order d, b, written CI(d, b) if (a) they are both integrated of order d, I(d) and (b) there exists some linear combination of the two series that is integrated of order d - b, where b gt 0.

ut Yt - ß0 - ß1Xt)No tendency to return to zero Error rarely drifts from zero 4Stationary Errors If we have two independent non-stationary series, then we may find evidence of a relationship when none exists (i.e. One way to test if there is a relationship between non- stationary data is if disequilibrium errors return to zero.

If long run relationship exists then errors should be a stationary series and have a zero mean.

Title: Cointegration in **Single** **Equations**: Lecture 5 1Cointegration in **Single** **Equations** Lecture 5 Introduction Using an Error Correction Model (ECM) assumes there is a long-run relationship between the variables in a **regression**.

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