Add Time varying regression TVRegression

[guilhermebodin]

No description provided.

[PaulMainwood]

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.