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Cointegration

# Cointegration - Economics 245B Cointegration Consider the...

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Economics 245B Cointegration Consider the linear regression model Y t = ° + X 0 t ± + U t : We are interested in the behavior of the OLS estimators of ° and ± . Recall from last time that the degree of dependence in the regressor and dependent variable play a key role in understanding adequate asymptotic approximations. We capture the serial correlation in the dependent variable (and regressor) with Y t = ²Y t ° 1 + V t : If j ² j < 1 , then the serial correlation is attenuated enough so that the series is stationary and standard asymptotic theory holds. If j ² j = 1 , then the serial correlation is so severe that the series is not stationary and alternative asymptotic theory must be used. To understand spurious regressions in full detail, we consider the case in which K = 1 and let Y t = Y t ° 1 + V 1 t and X t = X t ° 1 + V 2 t ; with V 1 t i.i.d. with mean 0 and variance ³ 2 1 , V 2 t i.i.d. with mean 0 and variance ³ 2 2 and V 1 t independent of V 2 t . Because V 1 t is independent of V 2 t , there is no relation between

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