🤖 AI Summary
This study addresses the challenge that traditional threshold time series models struggle to simultaneously capture both abrupt shifts and smooth evolution in threshold parameters. To overcome this limitation, the authors propose a time-varying threshold autoregressive model based on wavelet series expansion, which flexibly approximates irregular jumps and continuous variations in the threshold function. By leveraging the localized time-frequency properties of wavelet bases, the approach circumvents the limitations of Fourier-based methods in modeling local dynamics. Integrating wavelet expansion, a threshold mechanism, and an autoregressive structure, the proposed model demonstrates superior performance in both simulation studies and empirical analyses, achieving significantly higher fitting accuracy and forecasting capability compared to existing methods, thereby offering a novel framework for modeling complex nonlinear time series.
📝 Abstract
This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing greater flexibility than Fourier-based approaches. Simulation experiments and real-data applications are used to evaluate the model's performance.