# Write the Kalman filter equations for an (operatorname{AR}(1)) process written is state space form with (H_{t}=1, alpha_{t}=z_{t})

## Question:

Write the Kalman filter equations for an \(\operatorname{AR}(1)\) process written is state space form with \(H_{t}=1, \alpha_{t}=z_{t}\) and \(V_{t}=0, \Omega_{t}=\phi, R_{t}=\sigma_{a}^{2}\). Show that the Kalman gain is one in this case.

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**Related Book For**

## Statistical Learning For Big Dependent Data

**ISBN:** 9781119417385

1st Edition

**Authors:** Daniel Peña, Ruey S. Tsay