Two random walks with R² of 0.9 and no relationship
Asked at Two Sigma, Point72
You simulate two completely independent random walks (each day's value is the previous value plus fresh, unrelated noise) and regress one on the other. The often comes out at , , sometimes higher, with a "highly significant" t-statistic.
How can two unrelated series produce a huge , and what does this teach about trusting ?
Show a hint
measures how much of 's variation the line explains in-sample. A random walk wanders far from its mean. What does "variation around the mean" even mean for a series that trends?
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.