Statistical estimation of time-varying complexity in financial networks

Measuring Complexity in Financial Data

“…Third, for the BDM-based measure of complexity, implementation with more symbols may yield better results, although this would be computationally quite costly. Fourth, following Rai et al [27] we have shown that the heterogeneity of interaction strengths among the stocks significantly increases during the crisis period and attains an even higher level in the post-crisis period. Two major differences between our results and those of Rai et al [27] are that (i) in the present work, the spike in heterogeneity has a much FIGURE 3 | Evolution of the complexity of financial linkages among the stocks over the period 1972-2018 obtained from the BDM.…”

“…Fourth, following Rai et al [27] we have shown that the heterogeneity of interaction strengths among the stocks significantly increases during the crisis period and attains an even higher level in the post-crisis period. Two major differences between our results and those of Rai et al [27] are that (i) in the present work, the spike in heterogeneity has a much FIGURE 3 | Evolution of the complexity of financial linkages among the stocks over the period 1972-2018 obtained from the BDM. The dimension of the financial linkage data was reduced by mapping the dissimilarity matrices (constructed from the cross-correlation matrix ρ N×N as I N×N − ρ N×N ) onto two-dimensional grids using a multi-dimensional scaling technique, and the complexity measure was then evaluated on these.…”

“…Importantly, for us σ represents the heterogeneity in the strengths of connections of the interaction matrix Ŵ. In Rai et al [27] this idea was applied to the stock market with a discretetime formulation in the form of a vector autoregression (X t = ŴX t−1 + ǫ t , where one allows for a constant vector c in the vector autoregression estimation; see the Supplementary Material). It is shown that during times of crisis the estimated heterogeneity parameter (σ obtained from the estimatedŴ matrix) increases substantially.…”

“…It is shown that during times of crisis the estimated heterogeneity parameter (σ obtained from the estimatedŴ matrix) increases substantially. However, the data considered in Rai et al [27] was limited (spanning the 16 years 2002-17), the time windows were non-overlapping, and the analysis was done only on data from the New York Stock Exchange. In the present paper, we perform a complementary analysis with the same technique, using NASDAQ data from 1972 to 2018 with overlapping windows.…”

“…Finally, the fourth measure is based on the ecology-inspired dynamical systems theory proposed by Robert May [26]. In reference [27] an adaptation of the original May-Wigner result is proposed in the context of a discrete-time vector autoregression model and applied to a limited set of data from the New York Stock Exchange. We adopt the same approach and construct the implied heterogeneity index of stock interactions, which exhibits sharp transitions during the crisis and also in the post-crisis period, indicating lagged effects.…”