Investigate Threshold AR Models

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Introduce some non-linear time series models. Two-regime threshold AR (TAR) models are good candidates.

Original Paper :

Howell Tong
Department of Statistics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong

Tong, H. (1983) Threshold Models in Nonlinear Time Series Analysis. Lecture Notes in Statistics, Springer-Verlag

https://link.springer.com/book/10.1007/978-1-4684-7888-4
https://link.springer.com/chapter/10.1007/978-1-4684-7888-4_3

A good reference is given by :

Nonlinear Time Series Analysis

Author(s):Ruey S. Tay, Rong Chen

https://onlinelibrary.wiley.com/doi/book/10.1002/9781119514312

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Avoid reinventing the wheel.

Is there already a decent python implementation ?

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Impact on PyAF : TAR and TARX models.

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Model Parameters : Delay (d) and Threshold (r)

Explanation : Signal value d=7 days before was above or below threshold r => switch AR models.

The delay d has a functional meaning (business-related, control which AR model to use).

The threshold r can be chosen among signal quantiles (d = q_10, ...., q_90).

PyAF can generate different TAR models (test many values for d and r) simultaneously (parallelization OK).

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NTS: An R Package for Nonlinear Time Series Analysis

Xialu Liu,
Rong Chen,
R. Tsay

Published 2020

https://www.semanticscholar.org/paper/NTS%3A-An-R-Package-for-Nonlinear-Time-Series-Liu-Chen/ddb987d9afb86f55b7b46b1cf01e13bbc49af706

https://cran.r-project.org/web/packages/nlts/index.html