Time-varying higher moments in Bitcoin.

Cryptocurrencies represent a new and important class of investments but are associated with asymmetric distributions and extreme price changes. We use a modeling structure where higher-order moments (scale, skewness and kurtosis) are time-varying, and additionally we used nontraditional innovations distributions to study the return series of the most important cryptocurrency, Bitcoin. Based on the estimation of a series of Generalized Autoregressive Score (GAS) models, we compare predictive performance using a loss function based on Value at Risk performance.

Estimating spatiotemporal patterns of deaths by COVID-19 outbreak on a global scale.

OBJECTIVE: Our main objective is to estimate the trend of deaths by COVID-19 on a global scale, considering the six continents. STUDY DESIGN: The study design was a retrospective observational study conducted using the secondary data provided by the Our World in Data project on a public domain. SETTING: This study was conducted based on worldwide deaths by COVID-19 recorded for the Our World in Data project from 29 February 2020 to 17 February 2021. METHODS: Estimating the trend in COVID-19 deaths is not a trivial task due to the problems associated with the COVID-19 data, such as the spatial and temporal heterogeneity, observed seasonality and the delay between the onset of symptoms and diagnosis, indicating a relevant measurement error problem and changing the series' dependency structure. To bypass the aforementioned problems, we propose a method to estimate the components of trend, seasonality and cycle in COVID-19 data, controlling for the presence of measurement error and considering the spatial heterogeneity. We used the proposed model to estimate the trend component of deaths by COVID-19 on a global scale. RESULTS: The model was able to capture the patterns in the occurrence of deaths related to COVID-19, overcoming the problems observed in COVID-19 data. We found compelling evidence that spatiotemporal models are more accurate than univariate models to estimate the patterns of the occurrence of deaths. Based on the measures of dispersion of the models' prediction in relation to observed deaths, it is possible to note that the models with spatial component are significantly superior to the univariate model. CONCLUSION: The findings suggested that the spatial dynamics have an important role in the COVID-19 epidemic process since the results provided evidence that spatiotemporal models are more accurate to estimate the general patterns of the occurrence of deaths related to COVID-19.