Complexity-entropy causality plane: A useful approach to quantify the stock market inefficiency

Abstract

Nowadays we are often faced with huge databases resulting from the rapid growth of data storage technologies. This is particularly true when dealing with music databases. In this context, it is essential to have techniques and tools able to discriminate properties from these massive sets. In this work, we report on a statistical analysis of more than ten thousand songs aiming to obtain a complexity hierarchy. Our approach is based on the estimation of the permutation entropy combined with an intensive complexity measure, building up the complexity-entropy causality plane. The results obtained indicate that this representation space is very promising to discriminate songs as well as to allow a relative quantitative comparison among songs. Additionally, we believe that the here-reported method may be applied in practical situations since it is simple, robust and has a fast numerical implementation.

The (in)visible hand in the Libor market: an information theory approach

“…The planar representation of these quantifiers is introduced in efficiency analysis and has been successfully used to: rank efficiency in stock markets [43,45]; rank efficiency in commodity markets [44]; link informational efficiency with sovereign bond ratings [42]; and assess the impact of the establishment of a common currency and a deep and wide financial crisis in European sovereign bonds time series [10].…”

The Efficiency of Polish Stock Market: Ordinal Patterns Approach

“…Here, the data for dierent countries are grouped near the line from the left top to the right bottom. On the left, there are emergent markets (higher statistical complexity measure, lower normalized permutation entropy) and on the right developed ones (lower statistical complexity measure, higher normalized permutation entropy) [6]. There is a group of countries that are placed in the middle of complexity-entropy causality plane.…”

“…Thus, Zunino et al identied the third kind of market: hybrid. It takes intermediate values of statistical complexity measure and normalized permutation entropy and covers ten of the countries investigated in [6] (Argentina, Austria, Brazil, Canada, China, Greece, Hong Kong, Singapore, Taiwan and Turkey ve emergent and ve developed due to MSCI criterion). The position of Poland in complexity-entropy causality plane shows that it can be regarded as a country with the hybrid market, because it also takes intermediate values of statistical complexity measure and normalized permutation entropy (Fig.…”

“…Recent investigations of Zunino et al [5,6] have shown that ordinal patterns methods are very useful base to build various mathematical devices that classify markets according to their eciency. In [5,6] the authors analyzed 32 developed and emergent markets, using number of forbidden patterns, permutation entropy and statistical complexity measure.…”

“…In [5,6] the authors analyzed 32 developed and emergent markets, using number of forbidden patterns, permutation entropy and statistical complexity measure. In this paper we apply the same tools to study the eciency of Polish stock market, not mentioned in [5,6].…”