Improving the Process of Early-Warning Detection and Identifying the Most Affected Markets: Evidence from Subprime Mortgage Crisis and COVID-19 Outbreak-Application to American Stock Markets

Abstract

Stock-market-crash predictability is of particular interest in the field of financial time-series analysis. Famous examples of major stock-market crashes are the real-estate bubble in 2008 and COVID-19 in 2020. Several studies have studied the prediction process without taking into consideration which markets might be falling into a crisis. To this end, a combination analysis is utilized in this manuscript. Firstly, the auto-regressive estimation (ARE) algorithm is successfully applied to electroencephalography (EEG) brain data for detecting diseases. The ARE algorithm is employed based on state-space modelling, which applies the expectation-maximization algorithm and Kalman filter. This manuscript introduces its application, for the first time, to stock-market data. For this purpose, a time-evolving interaction surface is constructed to observe the change in the surface topology. This enables tracking of the stock market's behavior over time and differentiates between different states. This provides a deep understanding of the underlying system behavior before, during, and after a crisis. Different patterns of the stock-market movements are recognized, providing novel information regarding detecting an early-warning sign. Secondly, a Granger-causality time-domain technique, called directed partial correlation, is employed to infer the underlying interconnectivity structure among markets. This information is crucial for investors and market players, enabling them to differentiate between those markets which will fall in a catastrophic loss, and those which will not. Consequently, they can make successful decisions towards selecting less risky portfolios, which guarantees lower losses. The results showed the effectiveness of the use of this methodology in the framework of the process of early-warning detection.

Keywords: Granger-causality analysis; complex systems; expectation-maximization algorithm and kalman filter; financial markets; network analysis.

Figure 1

Kalman filter in the expectation-maximization algorithm. The Kalman filter is utilized to obtain conditional means using as parameters the $P\left(r\right)$ in every iteration r. Maximization of the expected value of the likelihood function leads to a new set of parameters $P(r+1)$ [26].

Figure 2

An illustrative diagram for the research methodology design utilized through the manuscript.

Figure 3

The constructed stock-market three-dimensional interaction parameter space, which corresponds to period (a) that represents the first half of 2006. This space was reconstructed based on the three estimated auto-correlation coefficients of the SSM model, where the estimate determines the coordinates of the position of each market. The figure demonstrates the level of interaction, which differs from one region to another. Note that the density bar is divided into three parts (low, medium, and high), with the corresponding interaction coefficients for each part. Therefore, the high-density spots correspond to high interaction among markets.

Figure 4

The constructed stock-market interaction network structure. The constructed network reflects the interaction structure among markets corresponding to region 1 in the constructed space presented in Figure 3. The red-colored nodes correspond to U.S. stock markets, while the green-colored node corresponds to a stock market belonging to Brazil. The causal strength of interest to be represented in this manuscript is above 0.65, reflecting strong interactions. More precisely, three kinds of strongly connected causal links are presented here. The first are the dashed links, which correspond to a causal strength between 0.65 and 0.74; the second are the light-colored links, which corresponds to a causal strength between 0.75 and 0.84, the third are the dark-colored links, which correspond to a causal strength between 0.85 and 0.95. The network shows that the majority of connected indices mostly belong to U.S. markets.

Figure 5

The constructed stock-market interaction network structure. The constructed network reflects the interaction structure among markets which corresponds to region 2 in the constructed space presented in Figure 3. The red-coloured nodes correspond to U.S. stock markets, the blue-colored node corresponds to a stock market belonging to Canada and the purple-colored node corresponds to a stock market belonging to Panama. Recall that the causal strength of interest to be represented in this manuscript is above 0.65. The network shows that the strong connectivity structure is captured between Panamanian and Canadian markets with U.S. markets.

Figure 6

The constructed stock-market three-dimensional interaction parameter space, which corresponds to period (b) that represents the second half of 2006 to the first half of 2007. This space is reconstructed based on the three estimated auto-correlation coefficients of the SSM model, where the estimate determines the coordinates of the position of each market. The figure shows that there is a region where the density is very high, which refers to strong interactions among stock markets.

Figure 7

The constructed stock-market interaction network structure. The constructed network reflects the interaction structure among markets corresponding to the high-density region in the constructed space presented in Figure 6. The red-colored nodes correspond to U.S. stock markets, the blue-colored nodes correspond to stock markets belonging to Canada, the green-colored nodes correspond to stock markets belonging to Brazil and the brown-colored nodes correspond to stock markets belonging to Colombia. The network shows that nodes 14, 15, 16 and 17 are the most interacting market indices with U.S. markets.

Figure 8

The topology of the constructed stock-market three-dimensional interaction parameter space, which corresponds to period (c) that represents the second half of 2007. Here, the whole market is in a state towards a crisis. The figure shows that there is a region in the middle of the space where the density is very high and wide, which is going in a specific direction, as indicated with an arrow.

Figure 9

The constructed stock-market interaction network structure. The constructed network reflects the interaction structure among markets corresponding to the high-density region, which spans the red region along the directed arrow in the constructed space presented in Figure 8. The red-colored nodes correspond to U.S. stock markets, the blue-colored nodes correspond to stock markets belonging to Canada, the green-colored nodes correspond to stock markets belonging to Brazil and the brown-colored nodes correspond to stock markets belonging to Colombia. The network shows that all other markets are strongly interconnected with U.S. market indicies.

Figure 10

The constructed stock-market three-dimensional interaction parameter space, which corresponds to period (d) that represents 2008. The figure shows that there is a region where the density is very high, as it refers to strong interactions among stock markets which are falling into a crisis forming a cluster.

Figure 11

The constructed stock-market interaction network structure. The constructed network reflects the interaction structure among markets corresponding to the high-density region, which spans the red region along the directed arrow in the constructed space presented in Figure 10. The red-colored nodes correspond to U.S. stock markets, the blue-colored nodes correspond to stock markets belonging to Canada, the green-colored nodes corresponding to stock markets belonging to Brazil and the brown-colored nodes correspond to a stock market belonging to Colombia. The network shows that nodes 13, 14, 15 and 16 are the most interacting market indices with U.S. markets.

Figure 12

The constructed stock-market three-dimensional interaction parameter space, when a crisis has ended for period (e) that represents the period (2009–2010). The figure shows that there is a region presented as a red curve where the topology of the density structure has changed from the ones observed before the crisis.

Figure 13

The constructed stock-market interaction network structure. The constructed network reflects the interaction structure among markets, which corresponds to the high-density region, which spans the red region along the directed arrow in the constructed space presented in Figure 12. The red-colored nodes correspond to U.S. stock markets, the blue-colored nodes correspond to stock markets belonging to Canada and the green-colored nodes correspond to stock markets belonging to Brazil. The network shows that there is no interesting pattern to be captured.

Figure 14

A summary graph of the results. The figure presents the combination of the three-dimensional interaction parameter spaces presented in Figure 6 and Figure 10. It shows that there is a transition occurring between two states, mainly the time before the crisis and the crisis time, forming two holes of clusters. This explains when the interactions among markets reach their peak, which, in turn, can be considered an indication that there is a potential crisis.

Figure 15

The constructed stock-market three-dimensional interaction parameter space. This is for all stages of the effect of COVID-19 crisis on stock markets. More precisely, sub-figure (a) shows the topology structure where no crisis occurs for the time period (1/10/2018 to 31/3/2019), sub-figure (b) shows the topology structure for the time period before crisis (1/4/2019 to 31/10/2019), sub-figure (c) shows the topology structure for the time towards crisis (1/11/2019 to 28/2/2020), sub-figure (d) shows the topology structure where the crisis occurs for the time period (1/3/2020 to 31/12/2020) and the final stage, the sub-figure (e) shows the topology structure for the time after crisis (2021). The figure shows how the topology of the interaction surface has changed from one state to another. The density regions, represented in dark brown, present the highest interactions between interaction coefficients 0.65 and 0.95. The transition occurred in stage (b) where the markets were towards falling into a crisis forming a clear cluster shown in stage (d).