Comments (1)
A big upvote for addition of this model.
Ideally, it would be based on the LocalLevelExplanatory model.
Quoting the doc string from LocalLevelExplanatory:
LocalLevelExplanatory(y::Vector{Fl}, X::Matrix{Fl}) where Fl
```math
A local level model with explanatory variables is defined by:
\begin{aligned}
y_{t} &= \mu_{t} + X_{1,t} \cdot \beta_{1,t} + \dots + X_{n,t} \cdot \beta_{n,t} + \varepsilon_{t} \quad &\varepsilon_{t} \sim \mathcal{N}(0, \sigma^2_{\varepsilon})\\
\mu_{t+1} &= \mu_{t} + \xi_{t} &\xi_{t} \sim \mathcal{N}(0, \sigma^2_{\xi})\\
\beta_{1,t+1} &= \beta_{1,t} &\tau_{1, t} \sim \mathcal{N}(0, \sigma^2_{\tau_{1}})\\
\dots &= \dots\\
\beta_{n,t+1} &= \beta_{n,t} &\tau_{n, t} \sim \mathcal{N}(0, \sigma^2_{\tau_{n}})\\\\
\end{aligned}
\end{gather*}
So the model could be made by making use of these \tau_{1} to \tau_{n}, and having the beta equations become:
\beta_{1, t+1} = \beta_{1, t} + tau_{1, t}
\dots &= \dots\\
\beta_{n, t+1} = \beta_{n, t} + tau_{n, t}
This would give a local level model with explanatory variables that allows time-varying regression values.
At the moment, I am still unable to get this working in versions 0.5.x (I think due to muddling myself setting the hyperparameters) so a worked out model would be hugely helpful.
Thank you for any attention you can give this.
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