Semiparametric outlier detection in nonstationary times series: Case study for atmospheric pollution in Brno, Czech Republic

Abstract Large environmental datasets usually include outliers which can have significant effects on further analysis and modelling. There exist various outlier detection methods that depend on the distribution of the analysed variable. However quite often the distribution of environmental variables can not be estimated. This paper presents an approach for identification of outliers in environmental time series which does not impose restrictions on the distribution of observed variables. The suggested algorithm combines kernel smoothing and extreme value estimation techniques for stochastic processes within considerations of nonstationary expected value of the process. The nonstationarity in variance is evaded by change point analysis which precedes the proposed algorithm. Possible outliers are identified as observations with rare occurrence and, in correspondence to extreme value methodology, the confidence limits for high values of observed variables are constructed. The proposed methodology can be especially convenient for cases where validation of the data has to be carried out manually, since it significantly reduces the number of implausible observations. For a case study, the technique is applied for outlier detection in time series of hourly PM 10 concentrations in Brno, Czech Republic. The methodology is derived on solid theoretical results and seems to perform well for the series of PM 10 . However its flexibility makes it generally applicable not only to series of atmospheric pollutants. On the other hand, the choice of return level turns out to be crucial in sensitivity to the outliers. This issue should be left to the practitioners to decide with respect to specific application conditions.