LongMemory.jl

Description

LongMemory.jl is a package to generate, estimate, and forecast long memory time series models.

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

The package is available in the Julia general registry and can be installed using the Julia REPL.

The repository is github.com/everval/LongMemory.jl and the documentation is everval.github.io/LongMemory.jl/.

Quick start

More information

A notebook with an illustrative example of the package can be found here.

Benchmarks comparing the package with other alternatives can be found here.

Paper

The official paper was published in the Journal of Open Source Software and can be downloaded here, while a paper with examples can be downloaded here.

Abstract

LongMemory.jl is a package for time series long memory modelling in Julia. The package provides functions to generate long memory, estimate model parameters, and forecast. Generating methods include fractional differencing, stochastic error duration, and cross-sectional aggregation. Estimators include the classic ones used to estimate the Hurst effect, those inspired by 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. This article presents the theoretical developments for long memory modelling, show examples using the data included with the package, and compares the properties of LongMemory.jl with current alternatives, including benchmarks. For some of the theoretical developments, LongMemory.jl provides the first publicly available implementation in any programming language. A notable feature of this package is that all functions are implemented in the same programming language, taking advantage of the ease of use and speed provided by Julia. Therefore, all code is accessible to the user. Multiple dispatch, a novel feature of the language, is used to speed computations and provide consistent calls to related methods. The package is related to the R packages longMemoryTS, fracdiff.