Journal of Statistical and Econometric Methods

An L1 smoother for outlier cleaning of time series

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  • Abstract

    This paper introduces a new robust outlier cleaner specific 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 fitting, by least absolute deviations, a reference function to the actual time series. Once the reference curve has been defined, it can be used to establish bands such that all observations that deviate from the reference curve by more than a prefixed 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 Classification: 90C05, 62M20, 37M10 
    Keywords: Linear programming, simultaneous prediction intervals, electricity prices, pre-processing time series.