Trend Filtering: Empirical Mode Decompositions versus ℓ1 and Hodrick-Prescott

Considering the problem of extracting a trend from a time series, we propose a novel approach based on empirical mode decomposition (EMD), called EMD trend filtering. The rationale is that EMD is a completely data-driven technique, which offers the possibility of estimating a trend of arbitrary shape as a sum of low-frequency intrinsic mode functions produced by the EMD. Based on an empirical analysis of EMD, an automatic procedure is proposed to select the requisite intrinsic mode functions. The performance of the EMD trend filtering is evaluated on simulated time series containing different forms of trends. Comparing furthermore to two existing techniques ( 1-trend filtering and Hodrick–Prescott filtering), we observe that the EMD trend filtering performs very similarly, while it does not require assumptions on the form of the trend and it is free from estimation parameters. We also illustrate the performance of the technique on the S&P 500 index, as an example of real-world time series.