RollingFunctions.jl
Roll a [weighted] function or run a statistic along windowed data.
Copyright © 20172023 by Jeffrey Sarnoff. Released under the MIT License.
works with integers, floats, and missings
works with unweighted data
 data that is a simple vector
 data that is a CartesianIndexed vector
works with weights
 weights given as a simple vector
 weights given as a kind of StatsBase.AbstractWeights
applies functions (1arg, .., 4args)
 applied over unweighted or weighted data
works with data matrices
 same 1arg function applied to each column
reasonable uses
 with a simple vector
 with a DataFrame column
 with a TimeSeries column
 with your own function
Rolling a function over data
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 unless the keyword padding
is given with the value to use for padding (e.g. missing
). Using padding
will fill the initial windowsize  1
values with that padding value; the result will match the length of the data.
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> result = rollmean(data, windowsize; padding=missing); print(result)
Union{Missing, Float32}[missing, missing, 2.0, 3.0, 4.0]
julia> weights = normalize([1.0f0, 2.0f0, 4.0f0])
3element Array{Float32,1}:
0.21821788
0.43643576
0.8728715
julia> result = rollmean(data, windowsize, weights); print(result)
Float32[1.23657, 1.74574, 2.25492]
julia> result = rollmean(data, windowsize, weights; padding=missing); print(result)
Union{Missing,Float32}[missing, missing, 1.23657, 1.74574, 2.25492]
Running a function over data
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> using RollingFunctions
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> using RollingFunctions
julia> using LinearAlgebra: normalize
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]
rolling stats
rollmin
,rollmax
,rollmean
,rollmedian
rollvar
,rollstd
,rollsem
,rollmad
,rollmad_normalized
rollskewness
,rollkurtosis
,rollvariation
rollcor
,rollcov
(over two data vectors)
running stats
runmin
,runmax
,runmean
,runmedian
runvar
,runstd
,runsem
,runmad
,runmad_normalized
runskewness
,runkurtosis
,runvariation
runcor
,runcov
(over two data vectors)
Some of these use a limit value for running over vec of length 1.
works with functions over 1, 2, 3 or 4 data vectors

rolling(function, data1, data2, windowsize)

rolling(function, data1, data2, windowsize, weights)
(weights apply to both data vectors) 
rolling(function, data1, data2, windowsize, weights1, weights2)

rolling(function, data1, data2, data3, windowsize)

rolling(function, data1, data2, data3, windowsize, weights)
(weights apply to all data vectors) 
rolling(function, data1, data2, data3, windowsize, weights1, weights2, weights3)

running(function, data1, data2, data3, data4, windowsize)

running(function, data1, data2, data3, data4, windowsize, weights)
(weights apply to all data vectors) 
running(function, data1, data2, data3, data4, windowsize, weights1, weights2, weights3, weights4)
!! CHANGE ME !!
Many statistical functions of two or more vector variables are not well defined for vectors of length 1.
To run these functions and get an initial tapered value that is well defined, supply the desired value as firstresult
.
running(function, data1, data2, windowsize, firstresult)
running(function, data1, data2, windowsize, weights, firstresult)
(weights apply to both data vectors)
Philosophy and Purpose
This package provides a way for rolling and for running a functional window over data. Data is conveyed either as a vector or as a means of obtaining a vector from a matrix or 3D array or other data structure (e.g. dataframes, timeseries). Windows move over the data. One may use unweighted windows or windows wherein each position carries weight. Weighted windows apply the weight sequence through the window as it moves over the data.
When a window is provided with weights, the weights should must be normalized. We provide an algorithmically safe normalizing function that you may rely upon. Adding the sequence of normalized values one to the next obtains 1.0 or a value very slightly less than 1.0  their sum will not exceed unity.
I do not know how to augment something already whole while respecting its integrity.
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 software exists to simpilfy some of what you create and to faciliate some of the work you do.
Some who use it insightfully share the best of that. Others write words that smile.
All of this is expressed through the design of RollingFunctions.
Also Consider
 The mapwindow function from ImageFiltering supports multidimensional window indexing and different maps.