Extracting Rules via Markov Chains for Cryptocurrencies Returns Forecasting.

With the growing popularity of digital currencies known as cryptocurrencies, there is a need to develop models capable of robustly analyzing and predicting the value of future returns in these markets. In this article, we extract behavior rules to predict the values of future returns in the Bitcoin, Ethereum, Litecoin, and Ripple closing series. We used categorical data in the analyses and Markov chain models from the first to the tenth order to propose a new way of establishing possible future scenarios, in which we analyze the dependence of memory on the dynamics of the process. We used the measurements of accuracy Mean Quadratic Error, Absolute Error Mean Percentage, and Absolute Standard Deviation for the choice of the best models. Our findings reveal that cryptocurrencies have long-range memory. Bitcoin, Ethereum, and Ripple exposed seven steps of memory, while Litecoin displayed nine memory steps. From the transitions between states that happened the most, we defined decision rules that assisted in the definition of future returns in the series. Our results can support the decisions of traders, investors, crypto-traders, and policy-makers.

Proposal of a non-linear model to adjust in vitro gas production at different incubation times

This work aims to propose a new model named Gompertz-Von Bertalanffy bicompartmental (GVB), a combination of the models Gompertz and Von Bertalanffy. The GVB models is applied to fit the kinetic curve of cumulative gas production (CGP) of four foods (SS ­ sunflower silage; CS ­ corn silage; and the mixtures 340SS ­ 660 gkg-1 of corn silage and 340 gkg-1 of sunflower silage; and 660SS ­ 340 gkg-1 of corn silage and 660 gkg-1 of sunflower silage). The GVB fit is compared to models Logistic-Von Bertalanffy bicompartmental (LVB) and bicompartmental logistic (BL). All the process studied employed the semi-automatic "in vitro" technique of producing gases used in ruminant nutrition. The gas production readout was performed at times 2, 4, 6, 8, 10, 12, 15, 19, 24, 30, 48, 72, and 96 h. The data generated were used to estimate the models' parameters by the least squared method with the iterative Gauss-Newton process. The data fit quality of the models was verified using the adjusted coefficient of determination criterion (), mean residual square (MRS), Akaike information criterion (AIC), and mean absolute deviation (MAD). Among the analyzed models, the LVB model presented the best quality of fit evaluators for CS. In contrast, the GVB model showed better quality of fit to describe CGP over time for 340SS, 660SS, and SS, presenting the highest values of () and the lowest values of MSR, AIC, and MAD.