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.

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.