HP Trend Filtering Using Gaussian Mixture Model Weighted Heuristic

Trends show the underlying structure of the time-series data. Trend estimation is a commonly used tool for financial market movement prediction. In traditional approaches, such as Hodrick-Prescott (HP) and L1 filtering, the trend is considered as a smoothed version of the time-series, including rare significant hills that are smoothed in the same way as usual noise. The goal of this paper is to allow the estimated trend to be more complex and detailed in the intervals of significant changes while making a smooth estimate in all other parts. This will be our main criteria for trend estimation. We present a modified version of HP weighted heuristic that provides the best trend according to the abovementioned criteria. Gaussian Mixture Models (GMMs) on the preliminary estimated trend are used in the weighted HP heuristic to decrease the penalty in the objective function for turning-point intervals. We conducted a set of experiments on financial datasets and compared the results with those obtained from the standard HP filtering with weighted heuristic. The results indicate an improvement in the cycling component using our proposed criteria compared to the HP filtering approach.