Bias-reduced (SIC)1-trend filtering

초록

The `1-trend filtering method is one of the most widely used methods for extracting underlying trends from noisy observations. Contrary to the Hodrick-Prescott filtering, the `1-trend filtering gives piecewise linear trends. One of the advantages of the `1-trend filtering is that it can be used for identifying change points in piecewise linear trends. However, since the `1-trend filtering employs total variation as a penalty term, estimated piecewise linear trends tend to be biased. In this study, we demonstrate the biasedness of the `1-trend filtering in trend level estimation and propose a two-stage bias-reduction procedure. The newly suggested estimator is based on the estimated change points of the `1-trend filtering. Numerical examples illustrate that the proposed method yields less biased estimates for piecewise linear trends.

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