New Proposals of a Stress Measure in a Capital and its Robust Estimator

TL;DR

This paper introduces a novel statistical shape-based stress measure for capital in economic systems, linking capital flows to internal stresses and proposing robust estimation methods validated on stock index data during the 2007 financial crisis.

Contribution

It presents a new shape-based stress functional and robust estimation methods for analyzing capital stresses, with empirical validation on stock market data.

Findings

Stresses in capital can be modeled using shape variability measures.

Capital flows are related to internal stresses analogous to heat.

Robust estimation methods effectively analyze stress during financial crises.

Abstract

In this paper a novel approach for a measurement of stresses in a capital, which induce the capital flows between economic systems, is proposed. The proposals appeal to an apparatus offered by the statistical theory of shape. We propose a stress functional basing on a concept of mean shape determined by representative particles of a capital carrier. We also propose methods of describing changes in an amount and a structure of stresses in a capital appealing, among others, to a Bookstein's pair of thin plain spline deformation, and a measure of a shape variability. We apply our approach to an indirect verification of the hypothesis according to which a capital flow between economic systems is related to an activity of an inner force related to stresses in a capital. We indicate, that the stresses create a phenomenon analogous to the heat, which may be interpreted in terms of a positive economic external effect, which attracts a capital from environment of a system to the system. For empirical studies we propose robust approach to estimate the stress functional basing on the data depth concept. In the empirical research we use data on five branch stock indexes from Warsaw Stock Exchange. The studied period involves the financial crisis of 2007.