In this paper the algorithm for ΔρDCCA statistical test (Guedes et al., 2018) [1] is presented. Our test begins with the simulation of four time series pairs, by an ARFIMA process. These time series has N=250, 500, 1000, and 2000 points, see Guedes et al. (2018) [1]. The probability distribution function (PDF) is made available for all 10,000 samples, that start from the original time series, in supplementary material.
h i g h l i g h t s• We analyze by DCCA cross-correlation coefficient the blue-chips companies in the Eurozone.• With the DCCA coefficient, we qualify and quantify how each blue-chip is adherent to its country index.• From this analysis, we can construct an adhesion map of each company with respect to the global index. In this paper we analyze the blue-chips (up to 50% of the total index) companies in the Eurozone. Our motivation being analysis of the effect of the 2008 financial crisis. For this purpose, we apply the DCCA cross-correlation coefficient (ρ DCCA ) between the country stock market index and their respective blue-chips. Then, with the cross-correlation coefficient, we qualify and quantify how each blue-chip is adherent to its country index, evaluating the type of cross-correlation among them. Subsequently, for each blue-chip, we propose to study the 2008 financial crisis by measuring the adherence between post and pre-crisis. From this analysis, we can construct an adhesion map of each company with respect to the global index. Our database is formed of 12 Eurozone countries.
h i g h l i g h t s • The BREXIT referendum is study by DFA method for the Euro zone. • In general, the referendum did not change efficiency levels significantly. • We also calculated the ∆ρ DCCA coefficient, and our results point to ∆ρ DCCA < 0. • This meaning that the UK is more segmented now than in the past.
This paper aims to analyze whether the financial crises of the past 20 years have reduced efficiency, in its weak form, in 19 stock markets belonging to the 20 most developed economies (G-20). The sample period comprises the period from 2 January 2000 to 5 February 2021 with the respective financial crises, namely, Dot-com, Argentina, Subprime, Sovereign debt, China stock market crash (2015–2016), UK’s withdrawal from the European Union and the global pandemic of 2020. The results highlight that most markets show signs of (in)efficiency in each sliding window (1000 days), that is, they show asymmetries and non-Gaussian distributions, and [Formula: see text]. These findings suggest that the random walk hypothesis is rejected in certain markets, which has implications for investors, since some returns may be expected, creating arbitrage and abnormal profit opportunities, contrary to the random walk and informational efficiency hypotheses. The results found also open room for market regulators to take steps to ensure better informational data across international financial markets.
In this paper, we implemented a new approach of measuring contagion effect on financial crisis based on the Detrended Multiple Cross-Correlation Coefficient, [Formula: see text], with a statistical test to assess its significance. Our study is restricted to the particular case in which three stock indexes are analyzed at the same time, with the results being divided into simulated and empirical cases. The simulated case was important to present the probability distribution function of [Formula: see text] and [Formula: see text], respectively, as well as confidence intervals for [Formula: see text]. The empirical case presents [Formula: see text] and [Formula: see text] for fourteen stock market indexes in the subprime crisis. With these applications, our study defines contagion effect on the financial system where crisis effect was perceived. In general, our results show the statistical significance of [Formula: see text], while measure of contagion effect depends on the size of the series and the time scale evaluated.
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