An L1 smoother for outlier cleaning of time series

Ilaria Lucrezia Amerise and Agostino Tarsitano

Journal of Statistical and Econometric Methods, 2020, vol. 9, issue 1, 3

Abstract: This paper introduces a new robust outlier cleaner speciï¬ c for high-frequency time series data and provides guidelines for researchers who wish to use this procedure before the analysis process starts. The essence of the method is a fully automatic, data-driven procedure based on ï¬ tting, by least absolute deviations, a reference function to the actual time series. Once the reference curve has been deï¬ ned, it can be used to establish bands such that all observations that deviate from the reference curve by more than a preï¬ xed amount will be replaced. Properties of the new screening tool are investigated through the accuracy of simultaneous prediction intervals produced by Box-Jenkins models applied to real data, before and after the outlier cleaner usage. It is shown that the new method can be validly used as a data preparation technique to ensure that statistical analysis is supported by clear-cut data.Mathematics Subject Classiï¬ cation: 90C05, 62M20, 37M10 Keywords: Linear programming, simultaneous prediction intervals, electricity prices, pre-processing time series.

Date: 2020
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