Long Memory
Documentation for LongMemory.jl.
Description
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.
Installation
The package is registered in the Julia registry and can be installed at the REPL with ] add LongMemory.
Generation
Long Memory Generation contains the documentation for the functions to generate time series long memory models.
Classic Estimation
Classic Estimator for the Hurst Effect contains the documentation for the functions to estimate the rescaled range (R/S) statistic and the Hurst coefficient.
Semiparametric Estimators
Semiparametric Estimators for Long Memory contains the documentation for the functions to estimate the long memory parameter based on the log-periodogram regression. Estimators include the Geweke and Porter-Hudak estimators and the Whittle estimator, as well as bias-reduced versions of them.
Parametric Estimation
Parametric Estimators for Long Memory contains the documentation for the functions to estimate time series long memory models by parametric methods. Of particular interest is the ARFIMA model. Moreover, a method to estimate the HAR model, a specification usually used as a proxy for long memory dynamics, is also available.
Forecasting
Forecasting Long Memory Processes contains the documentation for the functions to forecast long memory processes using the fractional differencing operator and the cross-sectional aggregation method. Forecasting using the HAR model is also available.
Data
Data Available contains the list of data sets available in the package.
Examples
You can follow this vignette to learn how to use the package.
List of Functions
Index contains the list of all the functions in the package.
Benchmarks
The following notebook contains benchmarks for some of the functions in the package against popular R packages: fracdiff and longMemoryTS.
Author
Citation
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}
}Report a bug
Please, report any bugs here.