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The spurious regression trap

You regress one random walk YtY_t on a second, completely independent random walk XtX_t (they share no common driver at all).

What tends to happen to the regression's tt-statistic and R2R^2, and why? How should the analysis be done instead?

Show a hint

Standard regression inference assumes stationary, well-behaved errors. Random walks violate that. Think about what happens to the usual standard-error formula when both series wander without bound.

Your answer

This one is open-ended. Work it through, then check your reasoning against the full solution.

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