Johansen arithmetic

For a pair of log prices with $T = 1{,}000$, Johansen's procedure gives eigenvalues $\hat\lambda_1 = 0.025$ and $\hat\lambda_2 = 0.004$. (a) Compute $\lambda_{\text{trace}}(0)$, $\lambda_{\max}(0)$ and $\lambda_{\text{trace}}(1)$. (b) Using the 5% critical values 15.49, 14.26 and 3.84, what rank does the sequential procedure select? (c) For two log stock prices, what does the selected rank imply, and what would you check before believing it?