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Abstract:
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In both environment and economic studies, the dilemma that multiple time series data with long-term trend including seasonality cannot be fully adjusted by the observed co-variates is often encountered. Long-term trend is complicated to determine and separate from abnormal short-term signals of interest. This paper addresses how to de-trend time series in order to recover abnormal short-term signals. It is found problematic that the current spline or kernel smoothing methods can produce either positive or negative significant associations from the same dataset, depending on how the smoothing parameters are chosen. To circumvent this problem, three classes of robust and stable smoothers are proposed. These smoothers can be applied without fine parameter tuning and efficiently estimate abnormal signals. Their properties are demonstrated by both case study (using design of experiment on scenarios) and simulation study (using synthetic datasets generated from the original dataset). Finally, general guidelines are provided on how to reveal abnormal signals from multiple time series data with long-term trend.
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