# Trouble replicating the experiments in “On-line Novelty Detection Using the Kalman Filter and Extreme Value Theory”

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 $$W_0$$?