A Julia package to deconvolve simple moving averages of time series.


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What UnrollingAverages.jl can do for you


UnrollingAverages is a Julia package aimed at deconvolving simple moving averages of time series to get the original ones back.

UnrollingAverages currently assumes that the moving average is a simple moving average. Further relaxations and extensions may come in the future, see Future Developments section.


Press ] in the Julia REPL and then

pkg> add UnrollingAverages


The package exports a single function called unroll: it returns a Vector whose elements are the possible original time series.

unroll(moving_average::Vector{Float64}, window::Int64; initial_conditions::U = nothing, assert_natural::Bool = false) where { U <: Union{ Tuple{Vararg{Union{Int64,Float64}}},Nothing} }


  • moving_average: the time series representing the moving average to unroll ;
  • window: the width of the moving average ;
  • initial_conditions: the initial values of the original time series to be recovered. It may be a Tuple of window-1 positive integer values, or nothing if initial conditions are unknown. Currently it is not possible to specify values in the middle of the time series, this may be a feature to be added in the future ;
  • assert_natural default boolean argument. If true, the pipeline will try to recover a time series of natural numbers only. More then one acceptable time series (where "acceptable" means that it reproduces moving_average) may be found and all will be returned.

A few remarks:

  1. If isnothing(initial_conditions):
    • if assert_natural, then an internal unroll_iterative method is called, which tries to exactly recover the whole time series, initial conditions included. Enter ?UnrollingAverages.unroll_iterative in a Julia to read further details;
    • if !assert_natural, then an internal unroll_linear_approximation method is called. See this StackExchange post. NB: this is an approximated method, it will generally not return the exact original time series;
  2. If typeof(initial_conditions) <: Ntuple{window-1, <:Union{Int64,Float64}}, then an internal unroll_recursive method is called, which exactly recovers the time series. Mathematical details about this function are reported in the documentation, and you may read more by entering ?UnrollingAverages.unroll_recursive.

Future Developments

  • Modify initial_conditions argument of unroll so that it accepts known values throughout the series ;
  • Implement reversing methods for other types of moving averages .

How to Contribute

If you wish to change or add some functionality, please file an issue. Some suggestions may be found in the Future Developments section.

How to Cite

If you use this package in your work, please cite this repository using the metadata in CITATION.bib.


Participating organisations

Interdisciplinary Physics Team (InPhyT)


Claudio Moroni
Claudio Moroni
Pietro Monticone
Pietro Monticone

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Updated 20 months ago