6. Outliers

Outliers, that is outlying observations, sometimes also known as aberrant observations, are being often studied in the literature closely related to missing data treatment and validation procedures. An interesting issue is concerned with the influence of outliers on the estimates of moments of the data distribution or indexes relevant for further data analysis and model building. The approach of robust statistics is oriented in such direction to ensure that good reliable estimates may be obtained even in the presence of gross errors or unusual measures originated by unexpected events. The approach we shall cope with here aims instead at discovering such outliers and either setting them apart or correcting them according to some properly fitted data model. The very complexity of such a problem prompted soon for employing general heuristic methods for outlier detection and size estimation for independent sample data. Owing to the dependence structure outlier analysis in time series proved to be much more difficult as observations have to be checked not only as regards their distance from the mean but as far as relationships among neighboring observations and correlation function are concerned. For this reason we shall give a brief account of evolutionary computing applications within independent data analysis framework while more detailed discussion will be devoted to outliers and influential observations in time series analysis.