Henderson Filters for Smoothing Economic and Market Time Series

Summary

Henderson filters are centered moving-average smoothers designed to preserve local cubic trends while reducing short-term irregular variation. Their weights are derived by minimizing the sum of squared third differences in the smoothed series. As a result, the filter reproduces a cubic polynomial without distortion and can pass trend-like cycles while suppressing very short fluctuations. The source notes their use in economic time-series analysis, including seasonal-adjustment workflows and trend estimation from seasonally adjusted data.

Weights are symmetric in the interior of a series, but asymmetric near its endpoints because observations on both sides are unavailable. Forecasting beyond the observed sample and then applying symmetric weights is one way to lessen this endpoint problem. The filter is centered, so recent estimates can change as new observations arrive; the post specifically cautions that it recalculates part of the recent bar history. The description gives no trading test or evidence that the smoother generates profitable signals, and its cited behavior concerns time-series smoothing rather than standalone trading rules.

Key ideas

• Henderson filters smooth a series while exactly reproducing local cubic polynomials.
• Their weights are chosen to minimize the squared third differences of the smoothed series.
• The filter reduces very short-term irregular variation while allowing trend cycles to pass through.
• Weights are symmetric in the middle of a series and asymmetric near its endpoints.
• Because the filter is centered, estimates for recent observations can be revised as new data arrives.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.