1. Introduction

Time series has a long history in social sciences, especially in economics and finance. As it is well known, much of economics and finances are concerned with modeling dynamics, and systematization of data over time was a subject that appeared early. In particular, two empirical topics become important when working with time series in social sciences: inferences and forecasting. The cumulated historical data permitted to applied statistical methods in order to find evidence of causation between social variables, finding some support to social theories. Considering the nonexperimental nature of the social sciences, this also encourages the development of statistical techniques. In fact, while in physics, it is relatively easy to get hundreds of thousands of data for a given time series, in economics there are often only 50 or 100 data for a time series, and maybe we can obtain thousands of data in financial series. For this reason, much of the statistical effort, in particular econometric effort was focused on developing powerful statistical tests, considering the availability of small samples. This is an important different approach between econometrics and for example, statistical mechanics in theoretical physics.

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We can identify two main groups in time series econometrics: univariate time series analysis concerning with techniques for the analysis of dependence in adjacent observations. It has increased importance since 1970 based on the main ideas underlying in [1]; multivariate time series analysis based on the vector autoregressive (VAR) models, made popular by [2]. In the first group, we find all the autoregressive integrated moving average (ARIMA) models and the related generalized autoregressive conditional heteroscedasticity (GARCH) models developed by [3]. The second group is a generalization of the AR models and we can find two important developments based on this: cointegration proposed by [4] focusing on finding a statistical relationship between variables; and noncausality test developed by [5], which takes the concept of predetermination try to test if a variable causes another. Much of the development in time series econometrics is found in books such as [6–18].

In summary, dependence and causation are two important topics in time series econometrics and time series analysis. These topics are related with the importance of inference and forecasting in social sciences. Econometrics has been focused in developing powerful test considering the available small samples. Most of these developments are based on linear models even if there are some developments considering nonlinearities; see for instance [19, 20].

Time series analysis in econometrics is mostly based on observations belonging to the set of the real numbers. Some variables can be categorical such as dummy variables. However, in this chapter, we will talk about a different approach that is known as symbolic time series analysis (STSA). It has been originally applied to physics and engineering as a statistical methodology to detect the very dynamic of highly noise time series. The application to social sciences such as economics or finance is very recent and there are some novel developments.

As mentioned before, the application of STSA in social sciences requires a different approach due to data limitation. In this sense, the design of powerful test considering the availability of data is crucial. As abovementioned, dependence and causation are two important topics. In this sense, we review an independence test and a first approach on testing noncausality, both based on STSA. The information theory was adopted as an approach to analyze the symbolic time series and the approximation of Shannon Entropy as an important measure, applied to test design.

The chapter is organized as follows. Section 2 presents the symbolic time series approach and its relation with the symbolic dynamics. In Section 3, we review some of the literature of STSA applied to the sciences. In Section 4, the information theory approach and Shannon Entropy measure is explained. Section 5 presents a review of the independence symbolic test. Section 6 focuses on causality test based on STSA. Section 7 discusses the difference between the proposed symbolic noncausality test and the traditional and well-known Granger noncausality test. Finally, in Section 8, we draw some conclusions and present some future lines of research.
