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 such as forecasting.
TrendDecomposition.jl is a Julia package for 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.
For now this package implements moving averages, simiple seaonal averages and based on that additive and multiplicative model decomposition. It also includes the Hodrick-Prescott (HP) filter as well as its generalization, generally known as Whittaker-Henderson smoothing, in this package named bohlmannFilter after its first inventor George Bohlmann.
In addition this module tries to implement also more novel approaches; so far the boosted HP Filter based on Peter Phillips and Zhentao Shi (2019): "Boosting the Hodrick-Prescott Filter" has been implemented.