ts_stable_space

A code repository to reproduce the results presented in the paper Over the Stability Space of a Multivariate Time Series.

Table of Contents

• Description
• Usage
• Example
• Contributing
• License

Description

The repository contains four main directories:

• source: This directory contains the source code for the algorithms implemented based on the article Over the Stability Space of a Multivariate Time Series. It includes the following files:

vectorial_methods.R: Implements the three methodologies proposed in the article for estimating the stable space of a multivariate time series.

simulations.R: Contains the main functions required to reproduce the simulation study presented in the article.

auxiliar_methods.R: Includes auxiliary functions for visualisation and error estimation.

• notebooks: This directory contains Jupyter notebooks that demonstrate the use of the source code and provide step-by-step instructions to reproduce the various tables and figures from the paper.

• databases: Contains all datasets used in the notebooks directory, including those for the practical examples.

• images: Contains the exact images used in the article. These can be reproduced using the notebooks, with some light post-processing. For instance, Figure_1.png and Figure_2.png are the result of running the notebook stability_space.ipynb four times and then combining the corresponding images.

Usage

To run the notebooks in the notebooks directory and the scripts in the source directory, use R version 4.1.2.

Enjoy it ☕

Example

Suppose we want to estimate the stability space of the following dataset using the three methodologies proposed in the article:

dt_inflation <- data.table::fread("../databases/variables_inflation.csv")

First, we define the input matrices for each method:

X_inflation <- as.matrix(dt_inflation, rownames = "Date")
rownames(X_inflation) <- NULL

Then, we run the following code lines—each corresponds to one of the methods:

# PLS, PCA
basis_inflation_PLS <- basis_stable(X_inflation, method = "pls")
basis_inflation_PCA <- basis_stable(scale(X_inflation), method="pca")

# SPCA
spca_para <- 1
basis_inflation_SPCA <- basis_stable(scale(X_inflation),method = "spca",
                                        spca_engine = "elasticnet",
                                        spca_sparse = "penalty",
                                        spca_para = spca_para)

# Johansen
basis_inflation_johansen <- basis_stable(X_inflation, method = "johansen")

Each basis_inflation_... object contains two elements: basis_S and basis_N, which represent the estimators of the stable space and the non-stable space basis, respectively.

Contributing

1. Fork the repository.
2. Create a new branch (git checkout -b feature-branch).
3. Commit your changes (git commit -m 'Add a new feature').
4. Push to the branch (git push origin feature-branch).
5. Open a Pull Request.

License

This project is licensed under the MIT License – see the LICENSE file for details.