PyTimeVar: A Python Package for Trending Time-Varying Time Series Models

Authors: Mingxuan Song (m3.song@student.vu.nl, Vrije Universiteit Amsterdam), Bernhard van der Sluis (vandersluis@ese.eur.nl, Erasmus Universiteit Rotterdam), and Yicong Lin (yc.lin@vu.nl, Vrije Universiteit Amsterdam & Tinbergen Institute)

Discussion paper titled "PyTimeVar: A Python Package for Trending Time-Varying Time Series Models" is available at https://tinbergen.nl/discussion-paper/6365/24-060-iii-pytimevar-a-python-package-for-trending-time-varying-time-series-models.

Purpose of the package

The PyTimeVar package offers state-of-the-art estimation and statistical inference methods for time series regression models with flexible trends and/or time-varying coefficients. The package implements nonparametric estimation along with multiple recently proposed bootstrap-assisted inference methods. Pointwise confidence intervals and simultaneous bands of parameter curves via bootstrap can be easily obtained using user-friendly commands. The package also includes four commonly used methods for modeling trends and time-varying relationships: boosted Hodrick-Prescot filter, power-law trend models, state-space models, and score-driven models. This allows users to compare different approaches within a unified environment.

The package is built upon several papers and books. We list the key references below.

Local linear kernel estimation and bootstrap inference

Friedrich and Lin (2024) (doi: https://doi.org/10.1016/j.jeconom.2022.09.004); Lin et al. (2025) (doi: https://doi.org/10.1080/10618600.2024.2403705); Friedrich et al. (2020) (doi: https://doi.org/10.1016/j.jeconom.2019.05.006); Smeekes and Urbain (2014) (doi: https://doi.org/10.26481/umagsb.2014008) Zhou and Wu (2010) (doi: https://doi.org/10.1111/j.1467-9868.2010.00743.x); Buhlmann (1998) (doi: https://doi.org/10.1214/aos/1030563978);

Boosted HP filter

Mei et al. (2024) (doi: https://doi.org/10.1002/jae.3086); Biswas et al. (2024) (doi: https://doi.org/10.1080/07474938.2024.2380704); Phillips and Shi (2021) (doi: https://doi.org/10.1111/iere.12495);

Power-law trend models

Lin and Reuvers (2025) (doi: https://doi.org/10.1111/jtsa.12805); Robinson (2012) (doi: https://doi.org/10.3150/10-BEJ349);

State-space models

Durbin and Koopman (2012) (doi: https://doi.org/10.1093/acprof:oso/9780199641178.001.0001);

Score-driven models

Creal et al. (2013) (doi: https://doi.org/10.1002/jae.1279); Harvey (2013) (doi: https://doi.org/10.1017/CBO9781139540933); Harvey and Luati (2014) (doi: https://doi.org/10.1080/01621459.2014.887011) Blasques et al. (2016) (doi: https://doi.org/10.1016/j.ijforecast.2015.11.018);

Features

• Nonparametric estimation of time-varying time series models, along with various bootstrap-assisted methods for inference, including local blockwise wild bootstrap, wild bootstrap, sieve bootstrap, sieve wild bootstrap, autoregressive wild bootstrap.
• Alternative estimation methods for modeling trend and time-varying relationships, including boosted HP filter, power-law trend models, state-space, and score-driven models. The package includes inference methods for power-law trend models, state-space models, and score-driven models.
• Unified framework for comparison of methods.
• Multiple datasets for illustration.

Getting started

The PyTimeVar can implemented as a PyPI package. To download the package in your Python environment, use the following command:

pip install PyTimeVar

Support

The documentation of the package can be found at the GitHub repository https://github.com/bpvand/PyTimeVar, and ReadTheDocs https://pytimevar.readthedocs.io/en/latest/.

For any questions or feedback regarding the PyTimeVar package, please feel free to contact the authors via email: m3.song@student.vu.nl; vandersluis@ese.eur.nl; yc.lin@vu.nl.