The ExponentialSmoothing function computes exponentially weighted moving averages for the original observations using the formula

where N is the number of elements in A and $S_1=A_1$ by default. This is useful for smoothing the data, thus eliminating cyclic and irregular patterns and therefore enhancing the long term trends.

The first parameter X is a single data sample - given as e.g. a Vector. Each value represents an individual observation.

The second parameter lambda is the smoothing constant, which can be any real number between 0 and 1.

For a more involved implementation of exponential smoothing, see TimeSeriesAnalysis[ExponentialSmoothingModel].

The options argument can contain one or more of the options shown below. These options are described in more detail in the Statistics[Mean] help page.

ignore=truefalse -- This option is used to specify how to handle non-numeric data. If ignore is set to true all non-numeric items in X will be ignored.

initial=deduce, or realcons -- This option is used to specify the initial value for the smoothed observations. By default, the first of the original observations is taken as the initial value.

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$A≔⟨\mathrm{seq}\left(\sin \left(i\right)\,i=1..100\right)⟩\:$

$U≔\mathrm{ExponentialSmoothing}\left(A\,0.2\right)\:$

$V≔\mathrm{ExponentialSmoothing}\left(A\,0.5\right)\:$

$W≔\mathrm{ExponentialSmoothing}\left(A\,0.2\,\mathrm{initial}=2\right)\:$

$\mathrm{LineChart}\left(\left[U\,V\,W\right]\right)$