Table 2.

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

Type	Information matrix entries
Step	${\mathcal{I}}_{1,2}/{\sigma }_{\mathbf{a}}^2={(1-{\theta }_1)}^{-2}(1-{\theta }^{n+1-T})$
	${\mathcal{I}}_{2,2}/{\sigma }_{\mathbf{a}}^2={(1-{\theta }_1^2)}^{-1}(1-{\theta }^{2(n+1-T)})$
Pulse	${\mathcal{I}}_{1,2}/{\sigma }_{\mathbf{a}}^2={(1-{\theta }_1)}^{-1}{\theta }_1^{n-T}$
	${\mathcal{I}}_{2,2}/{\sigma }_{\mathbf{a}}^2={(1+{\theta }_1)}^{-1}2(1+{\theta }^{2(n-T)+1})$
Ramp	${\mathcal{I}}_{1,2}/{\sigma }_{\mathbf{a}}^2={(1-{\theta }_1)}^{-3}(n+1-T+{\theta }_1^{n+2-T}-(n+2-T)\theta )$
	$\begin{array}{l}{\mathcal{I}}_{2,2}/{\sigma }_{\mathbf{a}}^2={(1+\theta )}^{-1}{(1-{\theta }_1)}^{-3}(2{\theta }^{2+n+T}(1+\theta )-{\theta }^{4+2n}\\ +{\theta }^{2T}(n+1-T-2\theta -(2+n-T){\theta }^2))\end{array}$

NOTE: For θ₁ = 0, set ${\theta }_1^0=1$. The 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, ${\mathcal{I}}_{1,1}/{\sigma }_{\mathbf{a}}^2=(n-1)/{(1-{\theta }_1)}^2$, and the (2, 1) entry is obtained by symmetry.