TST/CLN: roll_sum/mean/var/skew/kurt: simplification for non-monotonic indices
- [x] tests added / passed
- [x] passes `black pandas`
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`

The removed for-loop doesn't seem to be necessary (I hope this code is tested by an existing test).

I feel like I'm missing an obvious reason why these for-loops are needed: looking at the code I don't think we need them and the tests also pass.
there are exactly two tests that cover at least the sum part (mean/var/skew/kurtosis do not seem to be covered!).

The tests are `test_indexer_constructor_arg` and `test_indexer_accepts_rolling_args`, both from pandas/tests/window/test_base_indexer.py.

I will mark this PR as a draft and look into tests for these functions on the weekend.

I assume that the easiest way to trigger the non-monotonic branch for variable windows is by having a dataframe with a datetime index that is not sorted, or?

edit: I think the only way to trigger the variable non-monotonic part is through using a `BaseIndexer` with `rolling`. A `ValueError` is thrown for non-monotonic datetime.

 I printed the values I set to zero on master: they are zero. I assume the testcase has some randomness/platform-specific behavior? cc @mroeschke  cc @mroeschke  While we're addressing this

1. Could you name all the `is_monotonic_*` variables to `is_monotonic_increasing_*` just for clarity?
2. Could you see if we have tests for a monotonically decreasing index (and add some tests if there are none)? That's what should hit this code path > * Could you name all the `is_monotonic_*` variables to `is_monotonic_increasing_*` just for clarity?

Will do

> * Could you see if we have tests for a monotonically decreasing index (and add some tests if there are none)? That's what should hit this code path

I think the `not is_monotonic_bounds` branch calculates the requested statistic separately for each window (naive calculation but with cython) and is probably meant for non-monotonic bounds. If decreasing indices are common (they fall currently in the `not is_monotonic_bounds` branch), we could have a far better alternative:  re-use the `is_monotonic_bounds` branch but switch the `add_`/`remove_` calls?
 If you trace back the usage of `is_monotonic_bounds`, it checks the entire bounds at the start for monotonically increasing indexes.

I didn't implement the non-monotonic bound rolling case, but happy to change it if there a more efficient way to do it. > I didn't implement the non-monotonic bound rolling case

Isn't that already handled by the current `not is_monotonic_bounds` branch? Since that code calculates the statistic for each window completely independently, it can work with any windows.

I would have expected that `rolling` is much slower for decreasing indices as it processes windows independently of each other. At least in this simple test, that is not the case :)

```py
df = pd.DataFrame({'values': pd.np.random.rand(1000)})
df_reverse = pd.DataFrame({'values': df['values'][::-1]}, index=df.index[::-1])

%timeit df.rolling(window=10).mean()
645 µs ± 25.6 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

%timeit df_reverse.rolling(window=10).mean()
653 µs ± 21.4 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
``` kurt/skew are sometimes different between increasing/decreasing indices (at an order of 1-e8 for kurt and 1-e10 for skew). I would like to belief that the decreasing indices are more accurate as we set the accumulated value to zero instead of removing the to be deleted values.

@mroeschke is it okay to 1) use deterministic values for testing (instead of `np.random.rand`) 2) and then "fine-tune" the maximal difference to avoid failing the tests? > @mroeschke is it okay to 1) use deterministic values for testing (instead of np.random.rand) 2) and then "fine-tune" the maximal difference to avoid failing the tests?

Definitely, generally in favor of using deterministic values for testing vs np.random.rand should be good now :) @mroeschke @jreback  okay, I will manually compute the expected results.

About whatsnew: this PR doesn't add any new features and doesn't fix any bugs. Just tests and avoiding for-loops for non-increasing indices. > okay, I will manually compute the expected results.
> 
> About whatsnew: this PR doesn't add any new features and doesn't fix any bugs. Just tests and avoiding for-loops for non-increasing indices.

so results in 1.1.3 are ok, we just regressed somehow on master but haven't since haven't released 1.2 this is ok. great.

ping when ready. #37166 is going to rebase after this is in. rebased and added note that the expected statistics for sum/mean have been verified. @jreback green'ish (unrelated CI failure) Mind merging master and fixing up the code checks error? @mroeschke I think the code check errors are not caused by this PR. I rebased it now, let's see whether that fixes it. @mroeschke green except two unrelated windows CI failures Thanks @twoertwein. Awesome find and patch! 