Determining Generalized Threshold Structures in Threshold Autoregressive Models

Music City Center 

Threshold autoregressive (TAR) models are widely used in nonlinear time series analysis, where the autoregressive structure changes according to threshold variables. While previous studies have proposed methods for estimating threshold values, they generally assume that the threshold variable and autoregressive order are known. This study focuses on general scenarios where the threshold variable could be a linear combination of multiple lag variables and aims to address: (1) estimation of the threshold variable by finding the optimal linear combination coefficients, (2) determination of the autoregressive order, and (3) estimation of threshold values and determination of suitable regime number. For efficient computations, we adopt Bayesian optimization to determine threshold structures, which involves a re-parameterization transforming the parameter estimation problem into a model selection problem implemented via a greedy algorithm (Chan et al., 2017). The proposed methodology applies to univariate and multivariate time series and achieves an accurate threshold structure determination resulting in efficient forecasts, validated via simulation studies and applications.

Bayesian optimization

High-dimensional AIC

Threshold autoregression 

Business and Economic Statistics Section