I'm trying to replicate the online novelty detection algorithm from "On-line Novelty Detection Using the Kalman Filter and Extreme Value Theory" by Hyoung-joo Lee and Stephen J. Roberts. In the first paragraph of section 3, 'Experimental Results' the authors say they used a simple AR model in order to choose the model order $p$, initial state process noise $W_0$ and observation process noise $V_0$.

From what I can tell the state process noise matrix will be of a larger dimension than the observation process noise matrix ($W_0 \in \mathbb{R}^{2x2}$ in the case when $y_t \in \mathbb{R}$ from what I can tell). How is it possible to use an AR model of the observations to determine the $W_0$?


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