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Correction (and clarification) to EWMA doc (#26422)
* Correction (and clarification) to EWMA doc Correct ``adjust=True`` to ``adjust=False`` in line 889 of the documentation (discussing EWMA). Also propose minor clarifications in demonstration that two variants (adjust=False and adjust=True) are equivalent for infinite series (lines 868 and 887-893). * Removed trailing whitespace * Removed comma splice and added commas
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doc/source/user_guide/computation.rst

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@@ -865,7 +865,7 @@ which is equivalent to using weights
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The difference between the above two variants arises because we are
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dealing with series which have finite history. Consider a series of infinite
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history:
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history, with ``adjust=True``:
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.. math::
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@@ -884,10 +884,11 @@ and a ratio of :math:`1 - \alpha` we have
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&= \alpha x_t + (1 - \alpha)[x_{t-1} + (1 - \alpha) x_{t-2} + ...]\alpha\\
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&= \alpha x_t + (1 - \alpha) y_{t-1}
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which shows the equivalence of the above two variants for infinite series.
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When ``adjust=True`` we have :math:`y_0 = x_0` and from the last
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representation above we have :math:`y_t = \alpha x_t + (1 - \alpha) y_{t-1}`,
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therefore there is an assumption that :math:`x_0` is not an ordinary value
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which is the same expression as ``adjust=False`` above and therefore
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shows the equivalence of the two variants for infinite series.
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When ``adjust=False``, we have :math:`y_0 = x_0` and
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:math:`y_t = \alpha x_t + (1 - \alpha) y_{t-1}`.
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Therefore, there is an assumption that :math:`x_0` is not an ordinary value
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but rather an exponentially weighted moment of the infinite series up to that
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point.
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