The main goal of the paper is to show how mutual information can be used as a measure of dependence in financial time series. One major advantage of this approach resides precisely in its ability to account for nonlinear dependencies with no need to specify a theoretical probability distribution or use of a mean-variance model. r

In recent years there has been a closer interrelationship between several scientific areas trying to obtain a more realistic and rich explanation of the natural and social phenomena. Among these it should be emphasized the increasing interrelationship between physics and financial theory. In this field the analysis of uncertainty, which is crucial in financial analysis, can be made using measures of physics statistics and information theory, namely the Shannon entropy. One advantage of this approach is that the entropy is a more general measure than the variance, since it accounts for higher order moments of a probability distribution function. An empirical application was made using data collected from the Portuguese Stock Market.

a b s t r a c tThe daily closing prices of several stock market indices are examined to analyse whether noise reduction matters in measuring dependencies of the financial series. We consider the effect of noise reduction on the linear and nonlinear measure of dependencies. We also use singular spectrum analysis as a powerful method for filtering financial series. We compare the results with those obtained by ARMA and GARCH models as linear and nonlinear methods for filtering the series. We also examine the findings on an artificial data set namely the Hénon map.

Abstract. This paper presents a new test of independence (linear and nonlinear) among distributions, based on the entropy of Shannon. The main advantages of the presented approach are the fact that this measure does not need to assume any type of theoretical probability distribution and has the ability to capture the linear and nonlinear dependencies, without requiring the specification of any kind of dependence model.

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The maximum entropy principle can be used to assign utility values when only partial information is available about the decision maker's preferences. In order to obtain such utility values it is necessary to establish an analogy between probability and utility through the notion of a utility density function. In this paper we explore the maximum entropy principle to estimate the utility function of a risk averse decision maker.

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This study assesses the effects of the US financial and the Eurozone debt crises on a large set of frontier stock markets. Detrended Cross Correlation Analysis (DCCA) and Detrended Moving Cross Correlation Analysis (DMCA) are employed to investigate whether correlations between the crises-originating countries ts (US and Greece) and frontier stock markets increased from the calm to each crisis periods. Our results indicate that this was indeed the case and frontier markets were affected by both crises. DCCA and DMCA coefficients increased significantly for countries in Europe and also, although not so strongly, for Middle Eastern ones with the subprime crisis. In the case of the Eurozone debt crisis, the most affected countries were Slovenia, Romania, Nigeria, Kuwait, Oman and Vietnam. Evidence of contagion, using the test proposed by Guedes et al. (2018a, 2018b), is thus weaker in the case of the European debt crisis,leading to the conclusion that frontier stock markets were more affected by the US financial turmoil.