Effect of Data Transformations on Predictive Risk Indicators

Risk indicators used in many applications usually involve certain transformations of the variables of interest, such as averages or maxima over given time periods or spatial regions, threshold exceedances, etc., or a combination of them. A common practice is to predict these indicators by applying the same type of transformation on the sample data, that is, the ??historical?? values of the same indicators are used as the sample information set. In this work, the loss of information derived from the transformations defining the sample set is studied for different indicators and considering a flexible covariance model separating fractal dimension and memory. The evaluations and comparisons are performed in terms of predictive mutual information based on Shannon??s entropy. The results obtained for different scenarios suggest that, depending on the type of risk indicator considered and the dependence structure of the process of interest, the changes in terms of predictive information using diverse transformations of the observations may be substantial.