Elements in Econophysics – serie

Extreme events are ubiquitous in nature and social society, including natural disasters, accident disasters, crises in public health (such as Ebola and the COVID-19 pandemic), and social security incidents (wars, conflicts, and social unrest). These extreme events will heavily impact financial markets and lead to the appearance of extreme fluctuations in financial time series. Such extreme events lack statistics and are thus hard to predict. Recurrence interval analysis provides a feasible solution for risk assessment and forecasting. This Element aims to provide a systemic description of the techniques and research framework of recurrence interval analysis of financial time series. The authors also provide perspectives on future topics in this direction.

Classical mechanics provided the conceptual and methodological foundations of neoclassical economics, which has its roots in economic individualism. Since the early twentieth century, statistical mechanics has underpinned a lesser-known approach to economics and finance, one that focuses on aggregates and the interactions between individuals. This has led to the emergence of a new field of research, known as econophysics, which brings to the fore concepts such as emergent properties, power laws, networks, entropy, and multifractality, thereby reshaping economic enquiry.

This Element presents the κ-generalized distribution, a statistical model tailored for the analysis of income distribution. Developed over years of collaborative, multidisciplinary research, it clarifies the statistical properties of the model, assesses its empirical validity and compares its effectiveness with other parametric models. It also presents formulas for calculating inequality indices within the κ-generalized framework, including the widely used Gini coefficient and the relatively lesser-known Zanardi index of Lorenz curve asymmetry. Through empirical illustrations, the Element criticizes the conventional application of the Gini index, pointing out its inadequacy in capturing the full spectrum of inequality characteristics. Instead, it advocates the adoption of the Zanardi index, accentuating its ability to capture the inherent heterogeneity and asymmetry in income distributions.

Extreme events are ubiquitous in nature and social society, including natural disasters, accident disasters, crises in public health (such as Ebola and the COVID-19 pandemic), and social security incidents (wars, conflicts, and social unrest). These extreme events will heavily impact financial markets and lead to the appearance of extreme fluctuations in financial time series. Such extreme events lack statistics and are thus hard to predict. Recurrence interval analysis provides a feasible solution for risk assessment and forecasting. This Element aims to provide a systemic description of the techniques and research framework of recurrence interval analysis of financial time series. The authors also provide perspectives on future topics in this direction.