In this paper we investigate the relationship between the information entropy of the distribution of intraday returns and intraday and daily measures of market risk. Using data on the EUR/JPY exchange rate, we find a negative relationship between entropy and intraday Value-at-Risk, and also between entropy and intraday Expected Shortfall. This relationship is then used to forecast daily Value-at-Risk, using the entropy of the distribution of intraday returns as a predictor.

The Romanian health system is mainly public financed (80.45%) through the following sources: Social Health Insurance (65%), State and Local Authorities Budget (15.45%), while the private sources (voluntary health insurance and out of pocket) adds an additional 19.55% to the public funds. The shares of the types of expenditure reflect the importance of each sector in the overall health system, and trends in expenditure show the impact of financing on the health sector's structural changes. We analyzed the 20-year trend of the Social Health Insurance budget, from 1999 to 2019. The influences of the different allocations, subcategories, and new budget categories appearing over time were adjusted to reveal relevant trends. Of the 14 medical service categories and the stand-alone Administrative expenditure category, six expenditure categories including Hospital services, Total drugs, and Primary care showed stationary 20-year trends; five including Medical devices, Dialysis, and Homecare services showed ascendant trends; and four including Dentistry and Emergency services showed descendant trends. Stationary trends imply no structural changes in the health sector of relevant magnitude to impact the financing shares of major categories: hospitals, drugs, or primary care. Emerging trends related to the impact of different reforms were revealed only in the low share of expenditures categories. The allocation methodology and statistical analysis of the trends reveal a new perspective on the evolution of health sector in Romania.

This research provides insights for the separation of cryptocurrencies from other assets. Using dimensionality reduction techniques, we show that most of the variation among cryptocurrencies, stocks, exchange rates, commodities, bonds, and real estate indexes can be explained by the tail, memory and moment factors of their log-returns. By applying various classification methods, cryptocurrencies are categorized as a separate asset class, mainly due to the tail factor. The main result is the complete separation of cryptocurrencies from the other asset types, using the Maximum Variance Components Split method. Additionally, we show that cryptocurrencies tend to exhibit similar characteristics over time and become more distinguished from other asset classes (synchronic evolution).

In this paper we investigate the ability of several econometrical models to forecast value at risk for a sample of daily time series of cryptocurrency returns. Using high frequency data for Bitcoin, we estimate the entropy of intraday distribution of logreturns through the symbolic time series analysis (STSA), producing low-resolution data from high-resolution data. Our results show that entropy has a strong explanatory power for the quantiles of the distribution of the daily returns. Based on Christoffersen’s tests for Value at Risk (VaR) backtesting, we can conclude that the VaR forecast build upon the entropy of intraday returns is the best, compared to the forecasts provided by the classical GARCH models.