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### 8.14 Regularized Exponential Moving Average

The regularized exponential moving average (REMA) by Chris Satchwell is a variation on the EMA (see Exponential Moving Average) designed to be smoother but not introduce too much extra lag. The formula can be given in a number of forms, such as

```       Rp + alpha*(close - Rp) + lambda*(Rp + (Rp-Rpp))
REMA = ---------------------------------------------
1             +      lambda
```

alpha = N-day smoothing per EMA
Rp = yesterday’s REMA
Rpp = day before yesterday’s REMA
Lambda is a factor controlling the amount of “regularization”.

This form shows how there’s an Rp+alpha*(close-Rp) part like an EMA, and an Rp+(Rp-Rpp) part which projects from yesterday’s REMA according to whether it was rising or falling relative to the REMA of the day before. The two parts are averaged with a weighting 1 for the EMA part and lambda for the projection.

If lambda is zero then REMA is the same as a plain EMA. Satchwell suggests fairly small values for lambda, and the default in Chart is 0.5. John Ehlers noted that if lambda is large REMA becomes unstable.

In any case the result of the calculation is still an average of past prices with a certain set of weights that progressively decrease for older data. The following is the weights for N=15 and lambda=0.5,

#### 8.14.1 REMA Momentum

A momentum indicator is formed from REMA as the slope of the line from yesterday’s REMA to today’s.

```         REMA - REMAprev
RegMom = ---------------
REMAprev
```

This is like a Rate of Change (see Momentum and Rate of Change), but on just one day and as a fraction instead of a percentage. A crossing through zero of the RegMom is a peak or trough (and possibly just a flat spot before a further rise or fall in the REMA line).