What Is Cointegration?


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An (n x 1) vector tome series yt is said to be cointegrated if each of the series taken individually is non- stationary with unit root , while some linear combination of the series a'y is stationary for some nonzero (n x 1) vector a.

Cointegration is an econometric technique for testing the correlation between non- stationary variables. If two or more series are themselves non- stationary, but a linear combination of them is stationary, then the series is called co integrated.
The variable makes it stationary by difference d then it means it is integrated by difference one.

The purpose of cointegration is to make OLS a BLUE. Standard regression analysis is said to be best, linear, Unbiased. By taking non-stationary data in equation is not blue.
The co integration approach generally solves the problem by expanding the model into a system of equations in which each variable may influence every other variable. The statistical significance of the dependence of each variable on every other variable can then be tested
According to Engle and Granger definition of cointegration:

1. All components of xt are integrated of order d.
2. There exists a vector ' such that the linear combination 'xt
of order (d-b) where b> 0.

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