Fractional and fractal processes applied to cryptocurrencies price series.

Introduction: Cryptocurrencies have been attracting the attention from media, investors, regulators and academia during the last years. In spite of some scepticism in the financial area, cryptocurrencies are a relevant subject of academic research. Objectives: In this paper, several tools are adopted as an instrument that can help market agents and investors to more clearly assess the cryptocurrencies price dynamics and, thus, guide investment decisions more assertively while mitigating risks. Methods: We consider three methods, namely the Auto-Regressive Integrated Moving Average (ARIMA), Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) and Detrended Fluctuation Analysis, and three indices given by the Hurst and Lyapunov exponents or the Fractal Dimension. This information allows assessing the behaviour of the time series, such as their persistence, randomness, predictability and chaoticity. Results: The results suggest that, except for the Bitcoin, the other cryptocurrencies exhibit the characteristic of mean reverting, showing a lower predictability when compared to the Bitcoin. The results for the Bitcoin also indicate a persistent behavior that is related to the long memory effect. Conclusions: The ARFIMA reveals better predictive performance than the ARIMA for all cryptocurrencies. Indeed, the obtained residual values for the ARFIMA are smaller for the auto and partial auto correlations functions, as well as for confidence intervals.

The recovery of global stock markets indices after impacts due to pandemics.

The COVID-19 brings back the debate about the impact of disease outbreaks in economies and financial markets. The error correction terms (ECT) and cointegration processing tools have been applied in studies for identifying possible transmission mechanisms between distinct time series. This paper adopts the vector error correction model (VECM) to investigate the dynamic coupling between the pandemics (e.g., the COVID-19, EBOLA, MERS and SARS) and the evolution of key stocks exchange indices (e.g., Dow-Jones, S&P 500, EuroStoxx, DAX, CAC, Nikkei, HSI, Kospi, S&P ASX, Nifty and Ibov). The results show that the shocks caused by the diseases significantly affected the markets. Nonetheless, except for the COVID-19, the stock exchange indices reveal a sustained and fast recovering when an identical length time window of 79 days is analyzed. In addition, our findings contribute to point a higher volatility for all financial indices during the COVID-19, a strong impact over the Ibov-Brazil and its poor recover when compared to the other indices.