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.

To address the unknown nature of probability-sampling models, in this paper we use information theoretic concepts and the Cressie-Read (CR) family of information divergence measures to produce a flexible family of probability distributions, likelihood functions, estimators, and inference procedures. The usual case in statistical modeling is that the noisy indirect data are observed and known and the sampling model-error distribution-probability space, consistent with the data, is unknown. To address the unknown sampling process underlying the data, we consider a convex combination of two or more estimators derived from members of the flexible CR family of divergence measures and optimize that combination to select an estimator that minimizes expected quadratic loss. Sampling experiments are used to illustrate the finite sample properties of the resulting estimator and the nature of the recovered sampling distribution.

Time-series (TS) are employed in a variety of academic disciplines. In this paper we focus on extracting probability density functions (PDFs) from TS to gain an insight into the underlying dynamic processes. On discussing this “extraction” problem, we consider two popular approaches that we identify as histograms and Bandt–Pompe. We use an information-theoretic method to objectively compare the information content of the concomitant PDFs.

Although economic processes and systems are in general simple in nature, the underlying dynamics are complicated and seldom understood. Recognizing this, in this paper we use a nonstationary-conditional Markov process model of observed aggregate data to learn about and recover causal influence information associated with the underlying dynamic micro-behavior. Estimating equations are used as a link to the data and to model the dynamic conditional Markov process. To recover the unknown transition probabilities, we use an information theoretic approach to model the data and derive a new class of conditional Markov models. A quadratic loss function is used as a basis for selecting the optimal member from the family of possible likelihood-entropy functional(s). The asymptotic properties of the resulting estimators are demonstrated, and a range of potential applications is discussed.