A regression of \(Y_{t}\) onto current, past, and future values of \(X_{t}\) yields

\[ Y_{t}=3.0+1.7 X_{t+1}+0.8 X_{t}-0.2 X_{t-1}+u_{t} \]

a. Rearrange the regression so that it has the form shown in Equation (17.25). What are the values of \(\theta, \delta_{-1}, \delta_{0}\), and \(\delta_{1}\) ?

b. i. Suppose that \(X_{t}\) is \(I(1)\) and \(u_{t}\) is \(I(1)\). Are \(Y\) and \(X\) cointegrated?

ii. Suppose that \(X_{t}\) is \(I(0)\) and \(u_{t}\) is \(I(1)\). Are \(Y\) and \(X\) cointegrated?

iii. Suppose that \(X_{t}\) is \(I(1)\) and \(u_{t}\) is \(I(0)\). Are \(Y\) and \(X\) cointegrated?

Equation (17.25)

Transcribed Image Text:

Y = B +0X + 8AXj + ur j=-p