PyTimeVar 0.0.10

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.

# PyTimeVar: A Python Package for Trending Time-Varying Time Series Models <!– badges: start –> [](https://www.gnu.org/licenses/gpl-3.0)   <!– badges: end –>

Authors: Mingxuan Song ([e-mail], Vrije Universiteit Amsterdam), Bernhard van der Sluis ([e-mail], Erasmus Universiteit Rotterdam), and Yicong Lin ([e-mail], Vrije Universiteit Amsterdam & Tinbergen Institute)

## 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. (2024) (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); Bühlmann (1998) (doi: https://doi.org/10.1214/aos/1030563978);

### Boosted HP filter Mei et al. (2024) (doi: 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 (2024) (https://tinbergen.nl/discussion-paper/6214/22-092-iii-cointegrating-polynomial-regressions-with-power-law-trends-environmental-kuznets-curve-or-omitted-time-effects); 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-drive models Creal et al. (2013) (doi: https://doi.org/10.1002/jae.1279); Harvey (2013) (doi: https://doi.org/10.1017/CBO9781139540933);

## 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.

• 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: `python 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: [e-mail]; [e-mail]; [e-mail].