LongMemory.jl is a package for time series long memory modelling in Julia.

The package provides functions for generating long memory, estimating the parameters of the models, and forecasting.

Generating methods include fractional differencing, stochastic error duration, and cross-sectional aggregation.

Estimators include classic ones used to estimate the Hurst effect, those inspired by the log-periodogram regression, and parametric ones.

Forecasting is provided for all parametric estimators.

Moreover, the package adds plotting capabilities to illustrate long memory dynamics and forecasting.

Finally, the package includes the Nile River minima and Northern Hemisphere Temperature Anomalies data sets to illustrate the use of the functions.

The package is registered in the Julia General registry and can be installed with the Julia package manager.

From the Julia REPL, type ] to enter the Pkg REPL mode and run:

pkg> add LongMemory

Or, equivalently, via the Pkg API:

julia> import Pkg; Pkg.add("LongMemory")

Once installed, the package can be imported with the command:

julia> using LongMemory

The package documentation is available here or the link below.

An illustrative example of the package usage can be found here.

The following vignette contains benchmarks for some of the functions in the package against popular R packages: fracdiff and longMemoryTS.

If you use this package in your research, please cite it as:

Vera-Valdés, J.E. (2024). "LongMemory.jl: Generating, Estimating, and Forecasting Long Memory Models in Julia". arXiv 2401.14077. https://arxiv.org/abs/2401.14077

@article{VERAVALDES2024a,
title = {LongMemory.jl: Generating, Estimating, and Forecasting Long Memory Models in Julia},
year = {2024},
author = {Vera-Valdés, J.E.},
journal = {arXiv preprint arXiv:2401.14077},
url = {https://arxiv.org/abs/2401.14077}
}