Local level explanatory time varying

[PaulMainwood]

A new model - Local Level Explanatory allowing time varying regression coefficients.

Possible fix for issue #282 (though it is possible that you did not want a local level on that one - if not, could be addressed by setting sigma2_{\xi} = 0).

In Durbin/Koopmans' notation, the model is:

\begin{gather*}
    \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} &\tau_{1, t} \sim \mathcal{N}(0, \sigma^2_{\tau_{1}})\\
        \dots &= \dots\\
        \beta_{n,t+1} &= \beta_{n,t} + \tau_{n, t} &\tau_{n, t} \sim \mathcal{N}(0, \sigma^2_{\tau_{n}})\\\\
    \end{aligned}
\end{gather*}

The model automatically starts with all coefficients allowed to be time-varying. This can quickly lead to overfitting, so it is useful to fix one or more of the tau hyperparameters to zero to force those coefficients constant. With all taus set to zero, the model reduces to Local Level Explanatory.

(This is my first try at a pull request, so please do forgive lapses in etiquette / bad code / poor practices!)

[codecov]

Codecov Report

Merging #286 (9c00531) into master (b1723e7) will increase coverage by 0.11%.
The diff coverage is 100.00%.

❗ Current head 9c00531 differs from pull request most recent head 5acb6c5. Consider uploading reports for the commit 5acb6c5 to get more accurate results

@@            Coverage Diff             @@
##           master     #286      +/-   ##
==========================================
+ Coverage   93.88%   94.00%   +0.11%     
==========================================
  Files          33       34       +1     
  Lines        3043     3101      +58     
==========================================
+ Hits         2857     2915      +58     
  Misses        186      186              

Impacted Files	Coverage Δ
src/fit.jl	97.40% <ø> (ø)
src/models/locallevelexplanatorytimevarying.jl	100.00% <100.00%> (ø)

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[guilhermebodin]

Hi @PaulMainwood the PR looks good! Thank you for your contribution :) unfortunately you got an error on julia 1.0 ci.
Just a small request, if possible please bump the version on Project.toml from 0.5.17 to 0.5.18