Early warning of regime switching in a complex financial system from a spillover network dynamic perspective

Abstract

Early warning of regime switching in a complex financial system is a critical and challenging issue in risk management. Previous research has examined regime switching through analyzing the fluctuation features in a single point in time series; however, it has rarely examined the dynamic spillovers across multivariable time series. This paper develops an early warning model of regime switching that incorporates a spillover network model and a machine learning model. Typical energy prices and stock market indices are selected as the sample data. The key spillover networks can be detected according to the distribution of the network indicators. The early warning signals can be captured by six typical machine learning models, and the random forest model has better performance. The robustness of the model is also discussed. Our study enriches regime switching research and provides important early warning signals for policymakers and market investors.

Keywords: Business; Research methodology social sciences; Social sciences.

Graphical abstract

Figure 1

Detection of regime switching in a complex financial system (A) Spatial global residual entropy of the windowed time series. (B) Probability of two states. The window is the last day of the sub time series in the windowed time series. (C) The states of the windowed time series. The yellow and blue parts reflect the high and low states, respectively. The regime switching represents the switch between the high state and the low state.

Figure 2

An example of spillover networks The node in a subfigure is a financial time series, and the weighted edge denotes the direction and magnitude of spillover flow between two time series. (A) Spillover network during the global financial crisis. (B) Spillover network during the COVID-19 pandemic.

Figure 3

Dynamic topological structure of the spillover network The results are normalized network indicators (A) Dynamic diameter of the spillover network. Diam represents diameter (B) Dynamic APL of the spillover network. APL represents average path length. (C) Dynamic density of the spillover network. Dens represents density. (D) Dynamic AOS of the spillover network. AOS represents average out-strength. (E) Dynamic ABC of the spillover network. ABC represents average betweenness centrality. (F) Dynamic ACC of the spillover network. ACC represents average closeness centrality.

Figure 4

Distribution of the network indicators We define 0.1 as the interval extension of each network indicator to allocate the indicator into different intervals to analyze the relationship between the network indicator and its probability. The results are normalized network indicators. (A) Distribution of diameter. Diam represents diameter. (B) Distribution of APL. APL represents average path length. (C) Distribution of density. Dens represents density. (D) Distribution of AOS. AOS represents average out-strength. (E) Distribution of ABC. ABC represents average betweenness centrality. (F) Distribution of ACC. ACC represents average closeness centrality.

Figure 5

Dynamic F-measures of the training set and testing set in the machine learning models (A) Dynamic F-measures of the training set and testing set in the SVM. (B) Dynamic F-measures of the training set and testing set in the GBDT. (C) Dynamic F-measures of the training set and testing set in the ANN. (D) Dynamic F-measures of the training set and testing set in the DNN. (E) Dynamic F-measures of the training set and testing set in the RF. (F) Dynamic F-measures of the training set and testing set in the KNN.

Figure 6

Dynamic accuracies of the training set and testing set in the machine learning models (A) Dynamic accuracies of the training set and testing set in the SVM. (B) Dynamic accuracies of the training set and testing set in the GBDT. (C) Dynamic accuracies of the training set and testing set in the ANN. (D) Dynamic accuracies of the training set and testing set in the DNN. (E) Dynamic accuracies of the training set and testing set in the RF. (F) Dynamic accuracies of the training set and testing set in the KNN.

Figure 7

An example of the detection of early warning signals of regime switching The long line indicates regime switching, whereas the small line represents the early warning signals related to regime switching. (A) Early warning signals of regime switching on the training set. (B) Early warning signals of regime switching on the testing set.