Note
This package may be merged into a larger project in the future. However, it will remain available as a stand-alone package for users who prefer minimal dependencies. The current API is considered stable.
HamiltonFilters.jl is a lightweight implementation of the Hamilton
filter for time series analysis. It is not registered in the Julia
package registry, but can be installed directly from GitHub:
using Pkg
Pkg.add(url="https://github.com/enweg/HamiltonFilters.jl")To pin the package to a specific version:
Pkg.add(PackageSpec(url="https://github.com/enweg/HamiltonFilters.jl",
rev="v1.0.0"))Once installed, load the package with:
using HamiltonFiltersThe Hamilton filter estimates trend and cyclical components by running the following regression:
You must choose two parameters:
h: forecast horizonp: number of most recent values at timet(includingy_t)
Hamilton (2018) recommends:
| Frequency | h | p |
|---|---|---|
| Yearly | 2 | ? |
| Quarterly | 8 | 4 |
| Monthly | 24 | ? |
In general, he recommends that both h and p are integer multiples
of the number of observations in a year if the original data is
seasonal.
If the series is integrated of order d or stationary around a
d-th-order polynomial, choose p >= d to obtain a stationary cycle.
The cyclical component is defined as the regression residuals:
The trend is the difference between the observed data and the cycle.
Only observations starting from index p + h can be used for filtering.
Load the package:
using HamiltonFiltersConstruct a filter instance:
h = 8
p = 4
hfilter = HamiltonFilter(h, p)Apply the filter to a time series:
trend, cycle = filter(hfilter, data)The filter function always returns a tuple of the form (trend, cycle).
-
If
datais aVector{<:Real}, thentrendandcycleare vectors of the same length asdata. The first(p-1) + hvalues are filled withNaN. -
If
datais aMatrix{<:Real}, thentrendandcycleare matrices of the same size asdata. The filter is applied to each column independently, and the first(p-1) + hrows are filled withNaN. -
If
datais aDataFrame, thentrendandcycleare DataFrames of the same shape and with the same column names. The filter is applied column-wise, and the first(p-1) + hrows are filled withNaN.
Yes. The implementation has been compared to the hfilter function in
Matlab using real GDP data. The test folder contains:
logGDPC1.csv: log real GDP from FREDmatlab_hfilter.csv: Matlab output for comparison
The filter output matches the benchmark.