TrendDecomposition.jl
Welcome to the TrendDecomposition.jl documentation.
This is a preliminary version of the documentation. The package is also not feature complete until version 1.0, thus sometimes there are references to not yet implemented features.
TrendDecomposition.jl is a Julia package for the decomposition of time series into trend and cycle components. More generally it provides both (stochastic) trend component estimation and forecasting, though not all methods are suitable for forecasting.
By using filters and smoothers the most pragmatic approach to trend decomposition is estimating the trend $t$ and defining the cyclical component $c$ of time series $y$ as $c = y - t$. Often it is up to the user of this module to calculate the cyclical components themselves with the computed trend returned from a function provided by this module.
The following is a list of already implemented and documented methods:
Exponential Smoothing
- Simple exponential smoothing
- Double exponential smoothing / Brown linear method
- Holt Linear procedure
- Holt Winters method
Penalized smoothing
- Bohlmann Filter / Whittaker-Henderson Smoothing
- Leser / Hodrick-Prescott (HP) Filter
- Boosted HP Filter
- Taut string - piecewise constant / Total variation denoising
- L1 trend filtering with ADMM
- L1 trend filtering with ADMM using taut string
- L1 trend filtering with ADMM using fused Lasso
Moving Average (MA)
Seasonal Average
Classical Decomposition by moving averages
Examples, which demonstrate the usecase of some of the implemented methods, can be found in the Usage section.