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• W4220786039 abstract "Thanks to their simplicity and interpretable structure, auto-regressive processes are widely used to model time series data. However, many real time series data sets exhibit non-linear patterns, requiring non-linear modeling. The threshold Auto-Regressive (TAR) process provides a family of non-linear auto-regressive time series models in which the process dynamics are specific step functions of a thresholding variable. While estimation and inference for low-dimensional TAR models have been investigated, high-dimensional TAR models have received less attention. In this article, we develop a new framework for estimating high-dimensional TAR models, and propose two different sparsity-inducing penalties. The first penalty corresponds to a natural extension of classical TAR model to high-dimensional settings, where the same threshold is enforced for all model parameters. Our second penalty develops a more flexible TAR model, where different thresholds are allowed for different auto-regressive coefficients. We show that both penalized estimation strategies can be utilized in a three-step procedure that consistently learns both the thresholds and the corresponding auto-regressive coefficients. However, our theoretical and empirical investigations show that the direct extension of the TAR model is not appropriate for high-dimensional settings and is better suited for moderate dimensions. In contrast, the more flexible extension of the TAR model leads to consistent estimation and superior empirical performance in high dimensions." @default.
• W4220786039 created "2022-04-03" @default.
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• W4220786039 creator A5039697639 @default.
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• W4220786039 date "2022-01-01" @default.
• W4220786039 modified "2023-09-26" @default.
• W4220786039 title "Penalized estimation of threshold auto-regressive models with many components and thresholds" @default.
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• W4220786039 doi "https://doi.org/10.1214/22-ejs1982" @default.
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• W4220786039 hasPublicationYear "2022" @default.
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