add monthly AR1 process utilities (MESMER-group#473)

* add monthly AR1 process utilities

* add tests

* add new functions to stats init

* reshape AR output dims from year, month to time

* new drawing method and change in predict function

* add test for drawing

* remove buffer as multiple of 12

* extract drawing innovations

* comments and nits

* start autoregression at one

* allow covariance none

* adjust tests

* changelog

* documentation

* fixes

* make args in draw_autoregression_monthly keyword only

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Mathias Hauser <mathause@users.noreply.github.com>

CHANGELOG.rst

@@ -58,6 +58,12 @@ that this led to some numerical changes compared to the MESMER-M publication
   `#419 <https://github.com/MESMER-group/mesmer/pull/419>`_, and
   `#421 <https://github.com/MESMER-group/mesmer/pull/421>`_).
 
+**Auto-Regression**
+
+- Implement functions performing the monthly (cyclo-stationary) auto-regression and adapt these functions to
+  work with xarray. This includes extracting the drawing of spatially correlated innovations to a
+  stand-alone function. (`#473 <https://github.com/MESMER-group/mesmer/pull/473>`_)
+
 **Yeo-Johnson power transformer**
 
 -  Ensure the power transformer yields the correct normalization for more cases (

mesmer/stats/__init__.py

@@ -2,8 +2,11 @@
     _fit_auto_regression_scen_ens,
     _select_ar_order_scen_ens,
     draw_auto_regression_correlated,
+    draw_auto_regression_monthly,
     draw_auto_regression_uncorrelated,
     fit_auto_regression,
+    fit_auto_regression_monthly,
+    predict_auto_regression_monthly,
     select_ar_order,
 )
 from mesmer.stats._gaspari_cohn import gaspari_cohn, gaspari_cohn_correlation_matrices
@@ -22,6 +25,9 @@
     "draw_auto_regression_uncorrelated",
     "fit_auto_regression",
     "select_ar_order",
+    "fit_auto_regression_monthly",
+    "predict_auto_regression_monthly",
+    "draw_auto_regression_monthly",
     # gaspari cohn
     "gaspari_cohn_correlation_matrices",
     "gaspari_cohn",