hma

The Hull Moving Average reduces lag while maintaining smoothness by using weighted moving averages in a nested calculation. It achieves responsiveness by weighting recent data and using the square root of the period.

Parameters

• source (source): Data series to calculate HMA on - price field (close, open, high, low) or indicator output
• period (int): Number of periods for the moving average
• Common values: 9, 16, 20, 50, 200

Formula

HMA = WMA(2 * WMA(n/2) - WMA(n), sqrt(n))

Where:
- n = period
- WMA(n/2) = weighted MA with half period
- WMA(n) = weighted MA with full period
- Final WMA uses sqrt(n) as the period

Examples

hma(close, 9);  # 9-period Hull MA (fast, responsive)
hma(close, 20);  # 20-period Hull MA (standard)
x = hma(close, 50); close > x;  # Price above 50-period HMA

Returns

Hull moving average value with reduced lag compared to traditional MAs

Notes

• Uses WMA internally (3-level nested calculation)
• More responsive than SMA/EMA with similar smoothness
• sqrt(period) provides the smoothing in final step