Table 1.

Information Matrix for Simple Intervention Analysis With AR(1) Errors

Type	Information matrix entries
Step	${\mathcal{I}}_{1,2}/{\sigma }_{\mathbf{a}}^2=(n-T){(1-{\phi }_1)}^2+1-{\phi }_1$
	${\mathcal{I}}_{2,2}/{\sigma }_{\mathbf{a}}^2=(n-T){(1-{\phi }_1)}^2+1$
Pulse	${\mathcal{I}}_{1,2}/{\sigma }_{\mathbf{a}}^2=1-{\phi }_1^2$
	${\mathcal{I}}_{2,2}/{\sigma }_{\mathbf{a}}^2=1-{\phi }_1^2$
Ramp	${\mathcal{I}}_{1,2}/{\sigma }_{\mathbf{a}}^2=(1+n-T)(1-{\phi }_1)(2+n-T-(n-T){\phi }_1)/2$
	$\begin{array}{l}{\mathcal{I}}_{2,2}/{\sigma }_{\mathbf{a}}^2=(1+n-T)(6+7n+2n^2-7T-4nT+2T^2-8n{\phi }_1\\ -4n^2{\phi }_1+8T{\phi }_1+8nT{\phi }_1-4T^2{\phi }_1+n{{\phi }_1}^2+2n^2{\phi }_1^2-T{\phi }_1^2\\ -4nT{\phi }_1^2+2T^2{\phi }_1^2)/6\end{array}$

NOTE: This table gives the (1, 2) and (2, 2) entries, ${\mathcal{I}}_{1,2}/{\sigma }_{\mathbf{a}}^2$ and ${\mathcal{I}}_{2,2}/{\sigma }_{\mathbf{a}}^2$. For each intervention type, ${\mathcal{I}}_{1,1}/{\sigma }_{\mathbf{a}}^2=n{(1-{\phi }_1)}^2$, and the (2, 1) entry is obtained by symmetry.