cointegration_m-covrig.pdf - Time Series-2017 COINTEGRATION...

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Time Series, part 10, 2016-2017 1 COINTEGRATION Economic theory often suggests that certain pairs of economic or financial variables should be linked by a long-run economic relationship. Definition: The non-stationary time series t t X and t t Y , that are integrated of order 1,   1 ~ I X t t and   1 ~ I Y t t , are cointegrated if there is a linear combination of them, denoted t , t t t X Y 1 0 , such that t t is stationary, that is   0 ~ I t t . Let us recall that   1 ~ I X t t means that t t X is non-stationary, and t t X is stationary, that is   0 ~ I X t t , where 1 t t t X X X (the first order difference). Economically speaking, two variables will be cointegrated if they have a long-term, or equilibrium, relationship between them. Economic theory is often expressed in equilibrium terms, such as the permanent income hypothesis (PIH) that implies cointegration between consumption and income, nominal interest rates and inflation imports and exports. In the language of cointegration theory, a regression such as t t t X Y 1 0 is known as a cointegrating regression and the slope parameter 1 is known as the cointegrating parameter.
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Time Series, part 10, 2016-2017 2 One of the approaches for cointegration analysis: Engle-Granger approach: Cointegration in a single equation (Engle and Granger, 1987) Step 1. Testing for the existence of a cointegration relation between the two variables t X and t Y Step 1.1.
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