Ar forecasting example (#452)

* [Forecasting with AR models #450] first draft AR forecasting notebook

Signed-off-by: Nathaniel <[email protected]>

* [Forecasting with AR models #450] adding myst notebook

Signed-off-by: Nathaniel <[email protected]>

* [Forecasting with AR models #450] passing pre-commit checks

Signed-off-by: Nathaniel <[email protected]>

* [Forecasting with AR models #450] codespell check

Signed-off-by: Nathaniel <[email protected]>

* Update myst_nbs/time_series/Forecasting_with_structural_timeseries.myst.md

Co-authored-by: Luciano Paz <[email protected]>

* Update myst_nbs/time_series/Forecasting_with_structural_timeseries.myst.md

Co-authored-by: Luciano Paz <[email protected]>

* Update myst_nbs/time_series/Forecasting_with_structural_timeseries.myst.md

Co-authored-by: Luciano Paz <[email protected]>

* [Forecasting with AR models #450] changed AR predict process to be conditional on learned posterior

Signed-off-by: Nathaniel <[email protected]>

* [Forecasting with AR models #450] tidying text introducting the predict step pattern

Signed-off-by: Nathaniel <[email protected]>

* [Forecasting with AR models #450] remove some typos and add some more text

Signed-off-by: Nathaniel <[email protected]>

* [Forecasting with AR models #450] reverted coefs pattern in model and improved plot labels.

Signed-off-by: Nathaniel <[email protected]>

* updated with Ben's comments

Signed-off-by: Nathaniel <[email protected]>

* passing checks

Signed-off-by: Nathaniel <[email protected]>

* Update myst_nbs/time_series/Forecasting_with_structural_timeseries.myst.md

Co-authored-by: Luciano Paz <[email protected]>

* Update myst_nbs/time_series/Forecasting_with_structural_timeseries.myst.md

Co-authored-by: Luciano Paz <[email protected]>

* Update myst_nbs/time_series/Forecasting_with_structural_timeseries.myst.md

Co-authored-by: Luciano Paz <[email protected]>

* Update myst_nbs/time_series/Forecasting_with_structural_timeseries.myst.md

Co-authored-by: Luciano Paz <[email protected]>

* Update myst_nbs/time_series/Forecasting_with_structural_timeseries.myst.md

Co-authored-by: Luciano Paz <[email protected]>

* Update myst_nbs/time_series/Forecasting_with_structural_timeseries.myst.md

Co-authored-by: Luciano Paz <[email protected]>

* [Forecasting with AR models #450] fixed final prediction plot function and adjusted prediction step AR logic

Signed-off-by: Nathaniel <[email protected]>

* [Forecasting with AR models #450] corrected mistaken median prediction for mean and removed redundant argument from plot_fits function

Signed-off-by: Nathaniel <[email protected]>

Signed-off-by: Nathaniel <[email protected]>
Co-authored-by: Luciano Paz <[email protected]>

Author: NathanielF