Concept
Harmonic MA
Harmonic MA is a Trend concept. The Library holds 1 implementations, each one a working definition you can pull into Quant.
Top Harmonic MA indicators
1 total
What is a Harmonic MA?
A harmonic MA smooths price with the harmonic mean instead of the arithmetic mean: over an n-bar window it equals n divided by the sum of the reciprocals of the prices. It is one of the three Pythagorean means, and for any positive series it sits at or below the geometric MA, which in turn sits at or below the SMA; the three coincide only when every price in the window is identical.
Averaging reciprocals makes the harmonic mean disproportionately sensitive to the smallest values in the window: dips pull it down harder than spikes pull it up, and it is only defined for strictly positive data, since a value near zero would dominate it entirely. On ordinary price series, where values inside a window differ by small percentages, it plots almost on top of the SMA; differences become visible only when the window spans large swings. Statistically it is the p = -1 member of the power-mean family, with the arithmetic mean at p = 1 and the geometric mean as the limit at p = 0.
How traders use it
- As a variant smoother in generalized-mean studies that sweep the power parameter to compare arithmetic, geometric and harmonic responses on the same series.
- For averaging ratio-like series (valuation multiples, spreads, rates), where the harmonic mean is often the statistically appropriate average and the arithmetic mean overstates.
- As a conservative baseline when downside sensitivity is wanted: the line discounts upside outliers within its window rather than chasing them.
Related concepts · Moving-average lineage
Concept family
Trend
100 concepts mapped · 88 in the Library
Harmonic MA FAQ
How is a harmonic moving average calculated?
Invert each of the last n prices, average those reciprocals, then invert again: equivalently, n divided by the sum of 1/price across the window. It requires strictly positive inputs, since a zero breaks the reciprocal and values near zero drag the mean sharply lower. Weighted versions exist, but the plain form is the direct harmonic-mean analogue of a simple moving average.
When should you use a harmonic mean instead of an SMA on charts?
Rarely for plain price, where the two are nearly indistinguishable inside typical windows. The harmonic mean earns its place when averaging ratios (valuation multiples, spread ratios, rates), where it is often the mathematically apt mean, or when you deliberately want a smoother that leans toward the low values in the window. It is not a lag-reduction technique; its lag matches the SMA's.
Build Harmonic MA your way.
Quant writes, tests, and refines it with you — then it runs on LuxAlgo charting or ports to TradingView.