> *Wilder didn't like standard EMA weighting. He wanted history to decay slower. So he invented RMA, which is just EMA with a different alpha, confusing traders for 40 years.*
The Running Moving Average (RMA), also known as the Smoothed Moving Average (SMMA) or Wilder's Moving Average, is the backbone of J. Welles Wilder's most famous indicators: RSI, ATR, and ADX. It is functionally identical to an Exponential Moving Average (EMA), but with a smoothing factor ($\alpha$) of $1/N$ instead of $2/(N+1)$. This results in a longer "memory" and slower decay than a standard EMA of the same period.
## Historical Context
Introduced by J. Welles Wilder Jr. in his seminal 1978 book, *New Concepts in Technical Trading Systems*. Wilder developed his systems on a programmable calculator (the HP-67), where memory was scarce. The RMA allowed him to update averages without storing a history buffer, using a simple recursive formula. It remains the standard smoothing method for RSI and ATR.
## Architecture & Physics
RMA is an infinite impulse response (IIR) filter. In QuanTAlib, `Rma` is implemented as a zero-cost wrapper around the `Ema` class. It simply instantiates an `Ema` with a modified alpha.
### The Alpha Confusion
Traders often confuse RMA and EMA.
* **EMA**: $\alpha = \frac{2}{N+1}$
* **RMA**: $\alpha = \frac{1}{N}$
An RMA of period 14 is mathematically equivalent to an EMA of period 27 ($2N-1$).
## Mathematical Foundation
The recursive formula is identical to EMA, differing only in the weight.
1.**Initialization**: Like EMA, RMA requires a "warmup" period to converge. Wilder often initialized with a Simple Moving Average (SMA) of the first $N$ bars. QuanTAlib follows this convention.
2.**Naming**: Often called SMMA (Smoothed Moving Average) in other libraries.
