• data that is a simple vector
• data that is a CartesianIndexed vector

• weights given as a simple vector
• weights given as a kind of StatsBase.AbstractWeights

• with a simple vector
• with a DataFrame column
• with a TimeSeries column
• with your own function

With ndata = length(data), using a window of length windowsize, rolling a function results in a vector of ndata - windowsize + 1 elements. So there will be obtained windowsize - 1 fewer values than there are data values. All exported functions named with the prefix roll behave this way.

julia> data = collect(1.0f0:5.0f0); print(data)
Float32[1.0, 2.0, 3.0, 4.0, 5.0]
julia> windowsize = 3;

julia> result = rollmean(data, windowsize); print(result)
Float32[2.0, 3.0, 4.0]

julia> weights = normalize([1.0f0, 2.0f0, 4.0f0])
3-element Array{Float32,1}:
 0.21821788
 0.43643576
 0.8728715 
 
julia> result = rollmean(data, windowsize, weights); print(result)
Float32[1.23657, 1.74574, 2.25492]

To obtain the same number of output data values as are given, the initial windowsize - 1 values output must be generated outside of the rolling behavior. This is accomplished by tapering the needed values -- using the same function, rolling it over successively smaller window sizes. All exported functions named with the prefix run behave this way.

julia> data = collect(1.0f0:5.0f0); print(data)
Float32[1.0, 2.0, 3.0, 4.0, 5.0]
julia> windowsize = 3;

julia> result = runmean(data, windowsize); print(result)
Float32[1.0, 1.5, 2.0, 3.0, 4.0]

julia> weights = normalize([1.0f0, 2.0f0, 4.0f0]);
 
julia> result = runmean(data, windowsize, weights); print(result)
Float32[1.0, 1.11803, 1.23657, 1.74574, 2.25492]

• rollmin, rollmax, rollmean, rollmedian
• rollvar, rollstd, rollsem, rollmad, rollmad_normalized
• rollskewness, rollkurtosis, rollvariation

• runmin, runmax, runmean, runmedian
• runvar, runstd, runsem, runmad, runmad_normalized
• runskewness, runkurtosis, runvariation

Some of these use a limit value for running over vec of length 1.

• rolling(function, data, windowsize)
• rolling(function, data, windowsize, weights)
• running(function, data, windowsize)

• LinearAlgebra.normalize
• StatsBase: AbstractWeights, Weights
• StatsBase: FrequencyWeights, AnalyticWeights, ProbabilityWeights

This package provides an operational tensegrity. Within is a way for rolling and for running a functional window over data that is conveyed either as a vectorial sequence or as a means of obtaining that from a matrix or 3D array. One may use a windows that move over the data. One may use windows that are position weighted, applying the moving weight sequence to the windows that move over the data.

When running with a weighted window, the initial (first, second ..) values are determined using a tapering of the weighted window's span. This requires that the weights themselves be tapered along with the determinative function that is rolled. In this case, the weight subsequence is normalized (sums to one(T)), and that reweighting is used with the foreshortened window to taper that which rolls.

This work, and its upkeep (or its replacement by other's work), is offered as an appropriate and reliable scaffold. The work here is to be crisp, precise, accurate, and ever simplifying. There is no desire to repletify manners of handling here.

Some additional, small, purpose driven and providentially focused packages provide the meta-synthesis and enfolding dispatches that bring the more to the here.