Abstract
The focus of this paper is an information theoretic-symbolic logic approach to extract information from complex economic systems and unlock its dynamic content. Permutation Entropy (PE) is used to capture the permutation patterns-ordinal relations among the individual values of a given time series; to obtain a probability distribution of the accessible patterns; and to quantify the degree of complexity of an economic behavior system. Ordinal patterns are used to describe the intrinsic patterns, which are hidden in the dynamics of the economic system. Empirical applications involving the Dow Jones Industrial Average are presented to indicate the information recovery value and the applicability of the PE method. The results demonstrate the ability of the PE method to detect the extent of complexity (irregularity) and to discriminate and classify admissible and forbidden states.
Highlights
The 1000-point collapse of the Dow Jones Industrial Average on 6 May 2010 “ . . . was a small indicator of how complex and chaotic, in the formal sense, these systems have become . . . ”Ben Bernanke, Interview with the International Herald Tribune, 17 May 2010Economic behavioral processes and systems have the interesting characteristic of being stochastic, dynamic, seldom in equilibrium and not subject to a unique time invariant econometric model. the study of such systems has received a great deal of attention and various researchers have sought to develop economic tools to capture the complexity of real-world economic phenomena (LeBaron and Tesfatsion 2008), their underlying complex dynamics behavior is not well understood and it is difficult to model econometrically
We focus on an information theoretic-symbolic logic complexity approach in this paper, which resembles the method taken in ordinal time series analysis
In order to use the Bandt and Pompe (2002) Permutation Entropy (PE) methodology for evaluating the probability distribution P associated with the time series dynamical system under study, we start by considering the partitions of the pertinent D-dimensional space that will hopefully “reveal” relevant details of the ordinal structure of a given one-dimensional time series S(t) = { xt ; t = 1, · · ·, T }, with an embedding dimension D > 1 and time delay τ between xt values in the symbol sequences
Summary
The 1000-point collapse of the Dow Jones Industrial Average on 6 May 2010 “ . . . was a small indicator of how complex and chaotic, in the formal sense, these systems have become . . . ”. Despite the many productive efforts in this area of econometric reductionist modeling with a time series, the hidden dynamic nonlinear nonstationary temporal patterns underlying the time-dated outcomes have often remained hidden and have not provided a reliable basis for understanding the current economic behavioral processes and systems (Stiglitz 2018) Against this background, we focus on an information theoretic-symbolic logic complexity approach in this paper, which resembles the method taken in ordinal time series analysis (cf Bandt 2005; Bandt and Shiha 2007; Cao et al 2004; Hou et al 2017; Keller and Sinn 2005; Kowalski et al 2012; Zanin et al 2012; Zunino et al 2009, 2010b).
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