speedup auto_regression

[mathause]

Some profiling fun:

I tried to figure out why the tests/integration/test_calibrate_mesmer.py test are slowish. One main culprit is _fit_auto_regression_np and statsmodels: we need to set up the Autoreg model for each grid point individually, which checks the input every time, especially setting up the DeterministicProcess is slow. We can instantiate this once and pass it. This speeds up the tests by about 25% (from 12s to 8s or so). However, this does not seem to be recommended and is brittle (it copies implementation details). So I do not recommend to merge this PR (still would be nice to speed up this unnecessary slow repeated stuff...).

The code diff to profile is given below (and then visualize using snakeviz):

diff --git a/tests/integration/test_calibrate_mesmer.py b/tests/integration/test_calibrate_mesmer.py
index d374bce..04bf7b8 100644
--- a/tests/integration/test_calibrate_mesmer.py
+++ b/tests/integration/test_calibrate_mesmer.py
@@ -47,19 +47,31 @@ def test_calibrate_mesmer(
         "auxiliary",
     )

-    _calibrate_tas(
-        esms=test_esms,
-        scenarios_to_train=test_scenarios_to_train,
-        threshold_land=test_threshold_land,
-        output_file=test_output_file,
-        cmip_data_root_dir=test_cmip_data_root_dir,
-        cmip_generation=test_cmip_generation,
-        observations_root_dir=test_observations_root_dir,
-        auxiliary_data_dir=test_auxiliary_data_dir,
-        # save params as well - they are .gitignored
-        save_params=update_expected_files,
-        params_output_dir=params_output_dir,
-    )
+    from cProfile import Profile
+    from pstats import SortKey, Stats
+
+    with Profile() as profile:
+
+        _calibrate_tas(
+            esms=test_esms,
+            scenarios_to_train=test_scenarios_to_train,
+            threshold_land=test_threshold_land,
+            output_file=test_output_file,
+            cmip_data_root_dir=test_cmip_data_root_dir,
+            cmip_generation=test_cmip_generation,
+            observations_root_dir=test_observations_root_dir,
+            auxiliary_data_dir=test_auxiliary_data_dir,
+            # save params as well - they are .gitignored
+            save_params=update_expected_files,
+            params_output_dir=params_output_dir,
+        )
+
+        (
+            Stats(profile)
+            .strip_dirs()
+            .sort_stats(SortKey.CUMULATIVE)
+            .dump_stats("profile.out")
+        )

from cProfile import Profile
from pstats import SortKey, Stats

with Profile() as profile:
    
    function()

    (
        Stats(profile)
        .strip_dirs()
        .sort_stats(SortKey.CUMULATIVE)
        .dump_stats("profile.out")
    )

The visualization can be done with snakeviz