AdvancedMultiple choice
Two prices that wander together · Part 3 of 3
The log prices of two stocks each look like random walks: unit-root tests cannot reject a unit root in either. You regress one log price on the other in levels over five years of daily data and get an R² of 0.85 and a t-statistic of 25 on the slope.
The residual spread passes the test and behaves like an AR(1) with coefficient 0.95 per day. What is its half-life?
- AAbout 20 days, from 1/(1 − 0.95)
- BAbout 13.5 days
- CAbout 0.07 days, from ln 0.95 / ln 0.5
- DAbout 0.7 days, since ln 2 ≈ 0.69
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Unit roots, spurious regression and the basis of pairs trading
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