Indicator Formula
Technical Details — Running Moving Average (RMA)
Section titled “Technical Details — Running Moving Average (RMA)”Overview
Section titled “Overview”The Running Moving Average (RMA), also known as Wilder’s Smoothing, uses a smoothing factor of 1/n (compared to EMA’s 2/(n+1)). This produces a smoother, more stable average — RMA with period 14 is approximately equivalent to EMA with period 27.
Mathematical Derivation
Step 1 — Calculate First Value (SMA Seed)
Section titled “Step 1 — Calculate First Value (SMA Seed)”Purpose: Initialize using a simple average.
$$RMA[n] = \frac{\sum_{i=1}^{n} Close[i]}{n}$$
Where:
- $$n$$ = Period
What This Measures: Initial seed value using simple average
Step 2 — Apply RMA Recursion
Section titled “Step 2 — Apply RMA Recursion”Purpose: Blend new price using 1/n weighting.
$$RMA[t] = \frac{RMA[t-1] \times (n-1) + Close[t]}{n}$$
Where:
- $$RMA[t-1]$$ = Previous RMA value
- The effective alpha = 1/n
What This Measures: Smoothly decaying weighted average with less recent-price emphasis than EMA
Compact Formula Summary
$$RMA[t] = \frac{RMA[t-1] \times (n-1) + Close[t]}{n}$$
Equivalent: $$RMA[t] = RMA[t-1] + \frac{Close[t] - RMA[t-1]}{n}$$
Default Parameter: Period (n) = 14
Complete Calculation Example
If RMA[t-1] = 44.50, Close = 45.00, n = 14:
$$RMA = \frac{44.50 \times 13 + 45.00}{14} = \frac{578.50 + 45.00}{14} = \frac{623.50}{14} = 44.536$$
Compare: EMA with same inputs would give 44.59 — RMA moves more slowly.
Key Takeaways from the Example
- Slower Than EMA: RMA’s 1/n weighting is half the speed of EMA’s 2/(n+1) — smoother but laggier
- Used Inside Other Indicators: RSI and ATR use RMA internally for their smoothing
- Wilder’s Original: Created by J. Welles Wilder for use in RSI, ATR, and ADX calculations
- Period Equivalence: RMA(14) ≈ EMA(27) in terms of smoothness and responsiveness