medium · Quantitative Finance microstructure-arb
A pairs trader defines the spread as S_t = ln(P_A,t) - β ln(P_B,t).
Why is the use of logarithms generally preferred in cointegration modeling for equities?
- It eliminates entirely the need to separately run a Dickey-Fuller test on the resulting residual spread.
- It transforms the non-stationary I(1) price series into a stationary I(0) series immediately upon log transformation.
- It ensures the cointegrating vector represents a constant percentage relationship rather than a nominal price gap.
- It increases the speed of mean-reversion adjustment κ simply by shrinking the numerical scale of the underlying input data.
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