Penalized estimation of threshold auto-regressive models with many components and thresholds

Area of Science:

• Statistics
• Time Series Analysis
• Econometrics

Background:

• Autoregressive processes are standard for time series, but struggle with non-linear patterns.
• Threshold Auto-Regressive (TAR) models address non-linearity by using thresholding variables.
• High-dimensional TAR models remain underexplored compared to low-dimensional counterparts.

Purpose of the Study:

• To develop a novel framework for estimating high-dimensional TAR models.
• To propose and evaluate two distinct sparsity-inducing penalties for TAR models.
• To compare the performance of different TAR model extensions in high-dimensional settings.

Main Methods:

• Developed a new estimation framework for high-dimensional TAR models.
• Proposed two sparsity-inducing penalties: a shared threshold and a flexible multi-threshold approach.
• Utilized a three-step procedure for consistent estimation of thresholds and coefficients.

Main Results:

• The direct extension of TAR models with a shared threshold is unsuitable for high dimensions.
• The flexible TAR model extension with multiple thresholds demonstrates consistent estimation.
• Empirical results show superior performance of the flexible extension in high-dimensional scenarios.

Conclusions:

• The flexible threshold Auto-Regressive (TAR) model is more appropriate for high-dimensional time series.
• This research advances non-linear time series modeling in complex, high-dimensional data.
• The proposed methods offer improved accuracy and consistent estimation for challenging datasets.