RDP 9111: Monthly Movements in the Australian Dollar and Real Short-Term Interest Differentials: An Application of the Kalman Filter Equation (17)

\begin{array}{l} σ^{2} q_{(T)} = \frac{β^{2}}{{(1 - ρ)}^{2}} [λ^{2} σ_{2}^{2} + σ_{1}^{2}] (1 + ρ^{2} + ρ^{4} + \dots ρ^{2 (T - 1)}) + T σ_{3}^{2} \\ + \frac{2 β σ_{13}}{1 - ρ} (1 + ρ + ρ^{2} + \dots ρ^{T - 1}) \end{array}