The data file vec contains 100 observations on two generated series of data, \(x\) and \(y\). The variables are nonstationary and cointegrated without a constant term. Save the cointegrating residuals \((\hat{e})\) and estimate the VEC model. As a check, the results for the case normalized on \(y\) are

\[\begin{aligned}& \widehat{\Delta y_{t}}=-0.576\left(\hat{e}_{t-1}\right) \\& (t) \quad(-6.158) \\& \widehat{\Delta x_{t}}=0.450\left(\hat{e}_{t-1}\right) \\& (t) \quad(4.448)\end{aligned}\]

a. The residuals from the error correction model should not be autocorrelated. Are they?

b. Note that one of the error correction terms is negative and the other is positive. Explain why this is necessary.