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.

In this paper, we introduce a flexible and widely applicable nonparametric entropy-based testing procedure that can be used to assess the validity of simple hypotheses about a specific parametric population distribution. The testing methodology relies on the characteristic function of the population probability distribution being tested and is attractive in that, regardless of the null hypothesis being tested, it provides a unified framework for conducting such tests. The testing procedure is also computationally tractable and relatively straightforward to implement. In contrast to some alternative test statistics, the proposed entropy test is free from user-specified kernel and bandwidth choices, idiosyncratic and complex regularity conditions, and/or choices of evaluation grids. Several simulation exercises were performed to document the empirical performance of our proposed test, including a regression example that is illustrative of how, in some contexts, the approach can be applied to composite hypothesis-testing situations via data transformations. Overall, the testing procedure exhibits notable promise, exhibiting appreciable increasing power as sample size increases for a number of alternative distributions when contrasted with hypothesized null distributions. Possible general extensions of the approach to composite hypothesis-testing contexts, and directions for future work are also discussed.