Engle–Granger in practice

(a) Prove that in (13A.14) $\hat b - b = O_p(T^{-1})$ when the pair is cointegrated, and explain why this does not justify the OLS $t$-test on $\hat b$. (b) Why is the residual ADF regression run without a constant? (c) An analyst reports a residual ADF statistic of −3.10 for a pair of Indian bank stocks and calls it significant at 5% using the DF critical value −2.86. State the correct conclusion at 1%, 5% and 10%. (d) She screened 120 pairs and this was the most significant. What does that change?