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edited Apr 13, 2017 at 12:44

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In the following post post it was shown by mpiktas that the sample correlation of two I(1) series converge to a random variable. On the other, given two cointegrated I(1) variables the OLS estimator is super-consistent. How this two facts settle down together using the following relation between the OLS estimator $\hat {\beta}$ and the correlation?

$\hat {\beta} = {\rm cor}(Y_i, X_i) \cdot \frac{ {\rm SD}(Y_i) }{ {\rm SD}(X_i) }$

Thanks

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edited Dec 26, 2015 at 10:35

toroto

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asked Dec 25, 2015 at 16:41

toroto

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cointegration and correlation

In the following post it was shown by mpiktas that the sample correlation of two I(1) series converge to a random variable. On the other, given two cointegrated I(1) variables the OLS estimator is super-consistent. How this two facts settle down together using the following relation between the OLS estimator $\hat {\beta}$ and the correlation?

$\hat {\beta} = {\rm cor}(Y_i, X_i) \cdot \frac{ {\rm SD}(Y_i) }{ {\rm SD}(X_i) }$

Thanks

regression self-study cointegration

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cointegration and correlation