The MovingStatistic function computes moving statistics for a set of observations.

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

The second parameter m is the size of the moving window.

The third argument f is the statistic; can be any of the DescriptiveStatistics routines or a maple procedure which accepts a Vector and returns a floating point number.

Note that after f has been called on one subsample, the same Vector is reused for the next subsample, for efficiency reasons. All the builtin DescriptiveStatistics routines can handle this, but if you specify a custom maple procedure for f, you may need to copy its input Vector if you will need access to it after returning. See the example below for an explanation.

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

$A≔⟨\mathrm{seq}\left(\sin \left(i\right)\,i=1..20\right)⟩\:$

$U≔\mathrm{MovingStatistic}\left(A\,5\,\mathrm{Mean}\right)$

$U≔\begin{array}{c}\left[\begin{array}{c}0.0352323299444757\\ \mathrm{-0.188944966656889}\\ \mathrm{-0.239407132278267}\\ \mathrm{-0.0697594845655643}\\ 0.164024711544373\\ 0.247005344299126\\ 0.102890402628771\\ \mathrm{-0.135821500715074}\\ \mathrm{-0.249659742674422}\\ \mathrm{-0.133961968583799}\\ ⋮\end{array}\right]\\ \hfill \text{16 element Vector[column]}\end{array}$

$V≔\mathrm{MovingStatistic}\left(A\,5\,t\mapsto \mathrm{FivePointSummary}\left(t\,\mathrm{output}=\mathrm{maximum}\right)\right)$

$V≔\begin{array}{c}\left[\begin{array}{c}0.909297426825682\\ 0.909297426825682\\ 0.656986598718789\\ 0.989358246623382\\ 0.989358246623382\\ 0.989358246623382\\ 0.989358246623382\\ 0.989358246623382\\ 0.420167036826641\\ 0.990607355694870\\ ⋮\end{array}\right]\\ \hfill \text{16 element Vector[column]}\end{array}$

f := proc(A, q)
  Statistics[Quantile](A, q);
end proc:

$W≔\mathrm{MovingStatistic}\left(A\,5\,f\,0.3\right)$

$W≔\begin{array}{c}\left[\begin{array}{c}\mathrm{-0.770277280598276}\\ \mathrm{-0.770277280598276}\\ \mathrm{-0.770277280598276}\\ \mathrm{-0.770277280598276}\\ \mathrm{-0.324716083296540}\\ \mathrm{-0.297055872378289}\\ \mathrm{-0.574419050600125}\\ \mathrm{-0.574419050600125}\\ \mathrm{-0.574419050600125}\\ \mathrm{-0.574419050600125}\\ ⋮\end{array}\right]\\ \hfill \text{16 element Vector[column]}\end{array}$

$\mathrm{LineChart}\left(\left[A\,U\,V\,W\right]\,\mathrm{color}=\mathrm{red}..\mathrm{blue}\,\mathrm{thickness}=3\,\mathrm{legend}=\left[''original''\,''mean''\,''maximum''\,''quantile''\right]\right)$

$\mathrm{MovingStatistic}\left(⟨1\,2\,3⟩\,2\,g\right)$

$\left[\begin{array}{c}g\left(\left[\begin{array}{c}2\\ 3\end{array}\right]\right)\\ g\left(\left[\begin{array}{c}2\\ 3\end{array}\right]\right)\end{array}\right]$

$\mathrm{MovingStatistic}\left(⟨1\,2\,3⟩\,2\,v\mapsto g\left(\mathrm{copy}\left(v\right)\right)\right)$

$\left[\begin{array}{c}g\left(\left[\begin{array}{c}1\\ 2\end{array}\right]\right)\\ g\left(\left[\begin{array}{c}2\\ 3\end{array}\right]\right)\end{array}\right]$