Considerations developed on the transformations of time series by linear filters: theoretical and pratical aspects

The purpose of this work concerns the transformations of non-stationary time series using the known methods of filtering, in order to make stationary time series under investigation. It was therefore used the theory of linear systems to highlight the characteristics of the most used filters in the analysis of time series based on stochastic models of ARIMA type. In support of the first part mainly theoretical, we want to propose a comparative analysis of some well-known filtering operations on a number of time series of economic interest that have all the components of classical analysis of time series: trend in mean, seasonality and heteroscedasticity.