Add corr, cov, std & var to .rolling_exp

From the new routines in numbagg.

Maybe needs better tests (though these are quite heavily tested in numbagg), docs, and potentially need to think about types (maybe existing binary ops can help here?)

xarray/core/rolling_exp.py

@@ -194,3 +194,133 @@ def sum(self, keep_attrs: bool | None = None) -> T_DataWithCoords:
             on_missing_core_dim="copy",
             dask="parallelized",
         ).transpose(*dim_order)
+
+    def std(self) -> T_DataWithCoords:
+        """
+        Exponentially weighted moving standard deviation.
+
+        `keep_attrs` is always True for this method. Drop attrs separately to remove attrs.
+
+        Examples
+        --------
+        >>> da = xr.DataArray([1, 1, 2, 2, 2], dims="x")
+        >>> da.rolling_exp(x=2, window_type="span").std()
+        <xarray.DataArray (x: 5)>
+        array([       nan, 0.        , 0.67936622, 0.42966892, 0.25389527])
+        Dimensions without coordinates: x
+        """
+
+        if has_numbagg is False or has_numbagg < "0.4.0":
+            raise ImportError(
+                f"numbagg >= 0.4.0 is required for rolling_exp().std(), currently {has_numbagg} is installed"
+            )
+        dim_order = self.obj.dims
+
+        return apply_ufunc(
+            numbagg.move_exp_nanstd,
+            self.obj,
+            input_core_dims=[[self.dim]],
+            kwargs=self.kwargs,
+            output_core_dims=[[self.dim]],
+            keep_attrs=True,
+            on_missing_core_dim="copy",
+            dask="parallelized",
+        ).transpose(*dim_order)
+
+    def var(self) -> T_DataWithCoords:
+        """
+        Exponentially weighted moving variance.
+
+        `keep_attrs` is always True for this method. Drop attrs separately to remove attrs.
+
+        Examples
+        --------
+        >>> da = xr.DataArray([1, 1, 2, 2, 2], dims="x")
+        >>> da.rolling_exp(x=2, window_type="span").var()
+        <xarray.DataArray (x: 5)>
+        array([       nan, 0.        , 0.46153846, 0.18461538, 0.06446281])
+        Dimensions without coordinates: x
+        """
+
+        if has_numbagg is False or has_numbagg < "0.4.0":
+            raise ImportError(
+                f"numbagg >= 0.4.0 is required for rolling_exp().var(), currently {has_numbagg} is installed"
+            )
+        dim_order = self.obj.dims
+
+        return apply_ufunc(
+            numbagg.move_exp_nanvar,
+            self.obj,
+            input_core_dims=[[self.dim]],
+            kwargs=self.kwargs,
+            output_core_dims=[[self.dim]],
+            keep_attrs=True,
+            on_missing_core_dim="copy",
+            dask="parallelized",
+        ).transpose(*dim_order)
+
+    def cov(self, other: T_DataWithCoords) -> T_DataWithCoords:
+        """
+        Exponentially weighted moving covariance.
+
+        `keep_attrs` is always True for this method. Drop attrs separately to remove attrs.
+
+        Examples
+        --------
+        >>> da = xr.DataArray([1, 1, 2, 2, 2], dims="x")
+        >>> da.rolling_exp(x=2, window_type="span").cov(da**2)
+        <xarray.DataArray (x: 5)>
+        array([       nan, 0.        , 1.38461538, 0.55384615, 0.19338843])
+        Dimensions without coordinates: x
+        """
+
+        if has_numbagg is False or has_numbagg < "0.4.0":
+            raise ImportError(
+                f"numbagg >= 0.4.0 is required for rolling_exp().cov(), currently {has_numbagg} is installed"
+            )
+        dim_order = self.obj.dims
+
+        return apply_ufunc(
+            numbagg.move_exp_nancov,
+            self.obj,
+            other,
+            input_core_dims=[[self.dim], [self.dim]],
+            kwargs=self.kwargs,
+            output_core_dims=[[self.dim]],
+            keep_attrs=True,
+            on_missing_core_dim="copy",
+            dask="parallelized",
+        ).transpose(*dim_order)
+
+    def corr(self, other: T_DataWithCoords) -> T_DataWithCoords:
+        """
+        Exponentially weighted moving correlation.
+
+        `keep_attrs` is always True for this method. Drop attrs separately to remove attrs.
+
+        Examples
+        --------
+        >>> da = xr.DataArray([1, 1, 2, 2, 2], dims="x")
+        >>> da.rolling_exp(x=2, window_type="span").corr(da.shift(x=1))
+        <xarray.DataArray (x: 5)>
+        array([       nan,        nan,        nan, 0.4330127 , 0.48038446])
+        Dimensions without coordinates: x
+        """
+
+        if has_numbagg is False or has_numbagg < "0.4.0":
+            raise ImportError(
+                f"numbagg >= 0.4.0 is required for rolling_exp().cov(), currently {has_numbagg} is installed"
+            )
+        dim_order = self.obj.dims
+
+        return apply_ufunc(
+            numbagg.move_exp_nancorr,
+            self.obj,
+            other,
+            input_core_dims=[[self.dim], [self.dim]],
+            kwargs=self.kwargs,
+            output_core_dims=[[self.dim]],
+            keep_attrs=True,
+            on_missing_core_dim="copy",
+            dask="parallelized",
+        ).transpose(*dim_order)

xarray/tests/test_rolling.py

@@ -394,7 +394,7 @@ class TestDataArrayRollingExp:
         [["span", 5], ["alpha", 0.5], ["com", 0.5], ["halflife", 5]],
     )
     @pytest.mark.parametrize("backend", ["numpy"], indirect=True)
-    @pytest.mark.parametrize("func", ["mean", "sum"])
+    @pytest.mark.parametrize("func", ["mean", "sum", "var", "std"])
     def test_rolling_exp_runs(self, da, dim, window_type, window, func) -> None:
         da = da.where(da > 0.2)