Concept
Whittaker–Henderson Smoother
Whittaker–Henderson Smoother is a Trend concept. The Library holds 1 implementations, each one a working definition you can pull into Quant.
Top Whittaker–Henderson Smoother indicators
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What is the Whittaker–Henderson Smoother?
The Whittaker–Henderson smoother is a penalized least-squares method, proposed by Whittaker in 1923 and developed in actuarial graduation work by Henderson, that balances two competing costs: fidelity, the sum of squared differences between the smoothed series and the data, and roughness, the sum of squared differences of a chosen order (usually second or third) taken along the smoothed series itself. A single penalty parameter, commonly written lambda, sets the trade-off: larger values buy smoothness at the cost of fit, and the whole output is found at once by solving a banded linear system over the window.
That whole-window character is the key difference from moving averages and recursive filters: every point of the output depends on data before and after it, which makes the curve exceptionally smooth and nearly lag-free in the interior, but means the recent end recalculates as new bars arrive. The Hodrick-Prescott filter used in economics is the same construction with a second-order difference penalty.
How traders use it
- As a trend curve for analysis: applied to closes it yields a smooth centerline whose slope and turning points are far easier to read than raw price, useful for labeling regimes or studying past cycle turns.
- As the basis of an envelope: offsetting the smoothed curve by a volatility measure builds bands around a very quiet centerline, read the way other band systems are, with the end-point caveat in mind.
- As a pre-processing stage: feeding the graduated series into slope or momentum calculations cuts noise sharply, provided the workflow accounts for revisions at the fresh end of the window.
Related concepts · Digital filters & smoothers
Concept family
Trend
100 concepts mapped · 88 in the Library
Whittaker–Henderson Smoother FAQ
Does the Whittaker–Henderson smoother repaint?
The most recent portion does. Because each output point uses data on both sides of it, the newest values are provisional and shift as bars arrive, settling only once enough later data surrounds them. Sections deep inside the window are stable. Any signal logic built on the fresh end therefore needs repaint-safe handling or an evaluation delay.
How is Whittaker–Henderson smoothing different from a moving average?
A moving average is causal: each value is a weighted sum of past bars only, which is stable but lagged. Whittaker–Henderson solves for the entire smoothed series at once by penalizing roughness, so interior values use future as well as past data and show almost no lag. The price is end-point instability, whereas a moving average's plotted history never revises.
Build Whittaker–Henderson Smoother your way.
Quant writes, tests, and refines it with you — then it runs on LuxAlgo charting or ports to TradingView.