  Simple Exponential Smoothing is a classical technique used for smoothing time
series data by assigning exponentially decreasing weights to past observations
through a recursive equation; it is sometimes presented as a rule of thumb
procedure. We introduce a novel theoretical perspective where the recursive
equation that defines simple exponential smoothing occurs naturally as a
stochastic gradient ascent scheme to optimize a sequence of Gaussian
log-likelihood functions. Under this lens of analysis, our main theorem shows
that -- in a general setting -- simple exponential smoothing converges to a
neighborhood of the trend of a trend-stationary stochastic process. This offers
a novel theoretical assurance that the exponential smoothing procedure yields
reliable estimators of the underlying trend shedding light on long-standing
observations in the literature regarding the robustness of simple exponential
smoothing.
