The double quadratic uncertainty measures and their economic applications

Resumen

In the last few years there has been a tendency towards the study of statistical techniques and economic applications which provide more flexible methods than the traditional ones, such as the study of nonlinear models, the use of fuzzy sets, the development of fractional ARIMA models (ARFIMA) or the proposition of autoregressive conditional heteroskedasticity models (ARCH).This last contribution provides new methods of analyzing economic time series with time-varying volatility and his author R. Engle has been distinguished with the 2003 Nobel Prize in Economic Sciences.In this study two measures of information are presented: the double quadratic uncertainty and the double quadratic uncertainty involving utilities, studying their main properties.The double quadratic uncertainty is determined by two indexes in the family of uncertainty measures of order β introduced by [9]. The double quadraticuncertainty involving utilities is determined by two indicators in the family ofmeasures of uncertainty involving utilities of order β. Therefore both measuresof information could be considered as a fractional case of the families of theabove mentioned measures, providing expressions which in certain fields turnout to be more flexible and therefore more suitable to those family indicators.