Zunino et al. analyzed the problem of discrimination of developed and emergent markets by the use of ordinal patterns methods: number of forbidden patterns and ordinal pattern probability distribution as a basis for entropy and statistical measure of complexity. In this paper we apply the same methodology for the analysis of Polish stock market (index WIG). The results indicate that Polish market belongs neither to developed, nor to emergent groups of markets. It represents hybrid market, the third group distinguished in the paper by Zunino et al.
We performed statistical analysis on data from the Digg.com website, which enables its users to express their opinion on news stories by taking part in forum-like discussions as well as to directly evaluate previous posts and stories by assigning so called "diggs". Owing to fact that the content of each post has been annotated with its emotional value, apart from the strictly structural properties, the study also includes an analysis of the average emotional response of the comments about the main story. While analysing correlations at the story level, an interesting relationship between the number of diggs and the number of comments that a story received was found. The correlation between the two quantities is high for data where small threads dominate and consistently decreases for longer threads. However, while the correlation of the number of diggs and the average emotional response tends to grow for longer threads, correlations between numbers of comments and the average emotional response are almost zero. We also suggest presence of two different mechanisms governing the evolution of the discussion and, consequently, its length.
We perform a statistical analysis of emotionally annotated comments in two large online datasets, examining chains of consecutive posts in the discussions. Using comparisons with randomised data we show that there is a high level of correlation for the emotional content of messages.
Granger causality in its linear form has been shown by Barnett, Barrett and Seth [Phys. Rev. Lett. 103, 238701 (2009)] to be equivalent to transfer entropy in case of Gaussian distribution. Generalizations by Hlaváčková-Schindler [Appl. Math. Sci. 5, 3637 (2011)] are applied to distributions typical for biomedical applications. The financial returns, which are of great importance in financial econometrics, typically do not have Gaussian distribution. Generalizations leading to the concept of nonlinear Granger causality (e.g. causality in variance, causality in risk), known and applied in econometric literature, seem to be less known outside this field. In the paper an overview of some of the definitions and applications is given. In particular, we indicate some recent econometric results concerning application of the tests in linear multivariate framework. We emphasize importance of other variants of Granger causality, and need of development of methods reflecting features of financial variables.
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