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This paper has investigated the predictability of the top ten cryptocurrencies’ price dynamics, ranked by their daily market capitalization and trade volume, via the information theory quantifiers. Our analysis considers the Complexity-entropy causality plane to study the temporal evolution of the price of these cryptocurrencies and their respective locations along this 2D map, bearing in mind after and during the Russia-Ukraine war. Moreover, we apply the permutation entropy and the Jensen-Shannon statistical complexity measure to rank these cryptocurrencies similarly to a complexity hierarchy. Our findings reflect that the Russian-Ukraine war affects the informational efficiency of cryptocurrency dynamics. Specifically, the cryptocurrencies notably showed a decrease in informational inefficiency (USD-coin, Binance-USD, BNB, Dogecoin, and XRP). At the same time, the cryptocurrencies with more expressiveness for the financial market, considering the volume traded and the capitalized market, were strongly impacted, presenting an increase in informational inefficiency (Tether, Cardano, Ethereum, and Bitcoin). It clarifies the potential of cryptocurrencies to mitigate exogenous shocks and their capability to use with portfolio selection, risk diversification and herding behaviour.

Green bonds are financial assets similar to classic debt securities used to finance sustainable investments. Given this, they are a long-term investment alternative that effectively contributes to the planet’s future by preserving the environment and encouraging sustainable development. This research encompasses a rich dataset of equity and bond sectors, general indices, and the S&P Green Bond Index. We estimate the permutation entropy [Formula: see text], an appropriate statistical complexity measure [Formula: see text], and Fisher Information measure [Formula: see text]. Therefore, we employ these complexity measures to construct two 2D maps, the complexity-entropy causality plane ([Formula: see text] ×[Formula: see text]) and the Shannon–Fisher causality plane ([Formula: see text] ×[Formula: see text]). Also, we use the information theory quantifiers to rank these indices’ efficiency analogous to the complexity hierarchy. From a mathematical point of view, the complexity-entropy causality plane (CECP) is a map that considers the global analysis, while the SFCP is a map that simultaneously feels the global and local analysis. Our findings reveal that both 2D maps indicated the most efficient (b_info_tech) and least efficient (b_energy) assets. There are peculiarities in the ranking performed considering the information theory quantifiers used to build each map due to the mathematical distinction that underlies the construction of each map. Moreover, we applied two clustering approaches ([Formula: see text]-means and Hierarchical cluster) that categorically converged in the indication of four distinct groups, which allowed us to verify that, in an overview, equities present a unique dynamic when compared to bonds and the Green bond index.

This paper performs the asymmetric multifractal cross-correlation analysis to examine the COVID-19 effects on three relevant high-frequency fiat currencies, namely euro (EUR), yen (YEN) and the Great Britain pound (GBP), and two cryptocurrencies with the highest market capitalization and traded volume (Bitcoin and Ethereum) considering two periods (Pre-COVID-19 and during COVID-19). For both periods, we find that all pairs of these financial assets are characterized by overall persistent cross-correlation behavior [Formula: see text]. Moreover, COVID-19 promoted an increase in the multifractal spectrum’s width, which implies an increase in the complexity for all pairs considered here. We also studied the Generalized Cross-correlation Exponent, which allows us to verify that there is no asymmetric behavior between Bitcoin and fiat currencies and between Ethereum and fiat currencies. We conclude that investing simultaneously in major fiat currencies and leading cryptocurrencies can reduce the portfolio risk, leading to improvement in the investment results.

Independent of science branch, scientists have a consensus that peoples lives are highly susceptible to risk, and effectively quantifying risk is a big challenge. This paper assesses the Multifractal Cross-Correlation Measure (MRCC) among West Texas Intermediate (WTI), seven fiat currencies and three foreign exchange rates. Therefore, we use the Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) to examine the volatility dynamics considering the pairs of these financial records. We discover that all these volatility time series pairs [Formula: see text] are characterized by overall persistent behavior based on the values of [Formula: see text]. The MRCC values exhibit that the pairs WTI versus MXN [Formula: see text], WTI versus JPY [Formula: see text] and WTI versus NOK [Formula: see text] are more complex and persistent than the other pairs. Otherwise, the pairs WTI versus AUD [Formula: see text], WTI versus CAD [Formula: see text] and WTI versus EMK [Formula: see text] are less complex and persistent. Thus, our empirical findings shed light on the problem of quantification risk based on a multifractal perspective.

This research explores the predictability of the Brazilian inflation monthly price indexes time series by information theory quantifiers. Given this, we apply the Bandt and Pompe method to estimate the information theory quantifiers, specifically the Permutation entropy ([Formula: see text]) and the Fisher information measure ([Formula: see text]). Based on the values of both complexity measures, we construct the 2D plane called the Shannon-Fisher causality plane, which allows us to explore the disorder and quantify the randomness inherent to the temporal evolution of the significant Brazilian inflation indexes. Also, we apply [Formula: see text] and [Formula: see text] to rank the Brazilian inflation indexes based on the complexity hierarchy. An overview shows that the Brazilian inflation indexes display lower entropy which implies in higher predictability. The sliding window approach reveals that Brazilian inflation indexes (IPA, IPCA, IGP, IPC, and INPC) present decrease related to efficiency. The only exception is the INCC, which shows an increase in efficiency.

Cryptocurrencies play a pivotal role in the financial market. Given this, we perform the asymmetric multifractal cross-correlation analysis to examine the weak form of the Efficient Market Hypotheses (EMH) considering two temporal scales. In the daily scale, we find that the pair Bitcoin–Litecoin displays the largest multifractal spectrum. While, in the hourly scale, the pair Bitcoin–Ethereum presents the largest multifractal spectrum. Our empirical evidence has rejected the weak form of the EMH and clearly suggests that the dynamics of the analyzed cryptocurrency pairs are in line with the Fractal Market Hypothesis (FMH). Cross-correlation asymmetries are more persistent for small fluctuations than for large fluctuations. The results are essential for investors, portfolio and risk managers, and policymakers.