Sine-weighted MA

What is a Sine-weighted MA?

A sine-weighted MA (SWMA) is a windowed FIR moving average whose weights trace half a sine cycle across the lookback window. Each bar's weight is proportional to the sine of its fractional position in the window, so weights are near zero at both the oldest and newest bars and largest mid-window; the weighted sum is then normalized by the sum of the weights.

That half-sine taper makes it a close cousin of the Triangular MA: symmetric, center-weighted, and very smooth, with less ripple than an equal-weighted SMA because the soft window edges suppress the side lobes a rectangular window lets through. The cost is lag, roughly half the window length, since emphasis sits mid-window rather than on recent bars. It smooths better than it turns, which shapes where it is useful.

The design is borrowed straight from signal processing, where the half-sine is a standard window function. A rectangular window, which is what an SMA is, cuts the data off abruptly at both ends, and those hard edges leak high-frequency content through as ripple: small spurious wiggles in the plotted line that look like information but are artifacts of the window shape. Tapering the weights toward zero at the edges suppresses that leakage markedly, which is the entire engineering content of the SWMA: same length, same general lag class as the SMA, visibly calmer output.

In practice the SWMA, ported to the Library by everget and in layered form by blackcat1402, competes on one dimension only: smoothness per unit of complexity. It is not adaptive, not recency-weighted, and makes no attempt at lag reduction, so its natural jobs are the ones where jitter costs more than delay. A slow, steady line gives cleaner slope reads, steadier crossover legs, and calmer pre-smoothed input for downstream calculations, and the honest counsel is the mirror image: wherever early turn detection is the point, this is the wrong family.

How to identify a sine-weighted MA

The line looks like any smooth average; the signature is the weight shape and the behavior that follows from it.

1. 1Check the weight formula: weights proportional to the sine of each bar's fractional position across the window, peaking mid-window and tapering to near zero at both edges.
2. 2Confirm normalization: the weighted sum is divided by the sum of the weights, so the line stays on price scale.
3. 3Compare against an SMA of the same length: the SWMA should track the same path with visibly less bar-to-bar ripple and essentially the same lag.
4. 4Compare against recency-weighted averages: an EMA or WMA of similar smoothness will turn earlier; the SWMA's center weighting trades that speed away deliberately.
5. 5Watch the slope: the SWMA's derivative flips direction rarely and cleanly, which is exactly the property slope-based regime reads want.

How it's calculated

A moving average whose weights follow the first half-cycle of a sine wave, putting the most emphasis on the middle of the window.

Introduced by Patrick Lafferty in a 1999 Technical Analysis of Stocks and Commodities article.

Because the weights are symmetric rather than front-loaded, lag is close to an SMA of the same length and the weighting resembles a triangular MA; the benefit is smoother noise suppression, not less lag.

Not the same as the fixed 4-bar swma() built into some platforms, which uses weights 1/6, 2/6, 2/6, 1/6.

How traders use it

• As an extra-smooth trend baseline: the line's slope and price's side of it update with little bar-to-bar jitter, at the cost of confirming turns later than recency-weighted averages.
• As a pre-smoothing stage inside other studies, where the tapered window knocks down high-frequency noise before an oscillator or signal calculation runs on the result.
• As the slow leg in moving-average crossover systems where whipsaw suppression matters more than early entry, paired with a faster average for timing.
• As the input to an MA slope filter: because the sine taper suppresses ripple, slope-sign flips are rarer and more decisive, cutting the false regime changes a jumpier average generates.
• In crossover research as a controlled experiment: swapping an SMA slow leg for an SWMA of the same length isolates the effect of window shape on whipsaw, one of the few one-variable comparisons the moving-average zoo allows.

Sine-weighted MA vs other moving averages