Sufang An

The second and third authors, Sufang An and Zhiliang Dong, should be noted as shared co-corresponding authors on this work. Zhiliang Dong’s email address is: dongzhl@126.com. Reference 1. Wang L, An S, Dong Z, Dong X, Li J. Early warning of regime switching in a financial time series: A heteroskedastic network model. PLoS One. 2025;20(10):e0333734.

2 Methodology and measurement This section describes the methodology and process of studying financial time series. Fig 1 portrays the line of research in this paper. The entire research process is divided into four parts. First, the logarithmic yield time series is obtained from the original financial time series. The sliding window method cuts the logarithmic yield time series. Second, the parametric features of the time series under each window are extracted using the ARMA-GARCH model.