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Exponential smoothing based on L-estimation. (English) Zbl 1363.62114
Summary: Robust methods similar to exponential smoothing are suggested in this paper. First previous results for exponential smoothing in \(L_1\) are generalized using the regression quantiles, including a generalization to more parameters. Then a method based on the classical sign test is introduced that should deal not only with outliers but also with level shifts, including a detection of change points. Properties of various approaches are investigated by means of a simulation study. A real data example is used as an illustration.
MSC:
62M20 Inference from stochastic processes and prediction
62F35 Robustness and adaptive procedures (parametric inference)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
Software:
robustbase; Matlab
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