Forex Questions and Answers - FXAnswer

An exponentially smoothed moving average (ESMA) uses just the current closing price, the previous value of the ESMA, and a smoothing constant (SC) for the calculation:

ESMA(@) = SC*Close(@) +((1-SC)*ESMA(@)[-1])

Today’s ESMA is the sum of today’s closing price multiplied by the smoothing constant and yesterday’s ESMA multiplied by 1 minus the smoothing constant.

The smoothing constant can be any decimal number between zero and 1. Traders use a formula for the smoothing constant to approximate a simple moving average, 2/(n + 1) where n is the lookback period used in an SMA. If we set n = 5, then 2/(n+ 1) =2/6 = 0.3333. The formula for the five-day ESMA:

ESMA(@) = 0.3333*Close(@) +(1-0.3333)*ESMA(@)[-1]

To easily see how the formula for the smoothing constant approximates a simple moving average, consider that a one-day SMA is simply the closing price and if we use n = 1 in the ESMA, the smoothing constant is 2/(1+1) = 2/2 =1. The ESMA then is:

ESMA(@) = 1*Close(@) +(1-1)*ESMA(@)[-1]
ESMA(@) = 1*Close(@) +(0)*ESMA(@)[-1]
ESMA(@) = Close(@)

In addition, note that the ESMA is the sum of the adjusted current closing price and the adjusted previous ESMA. This leads to a change in direction immediately by the ESMA if the closing price is above or below the ESMA for the first time. In other words, the first day the close is above a falling ESMA will cause the ESMA to turn up on that day. The ESMA does not lag the change in the direction in the market the way an SMA can.

Source(s):

http://www.cqg.com/Technical-Analysis/Studies/ Standard-Studies/Moving-Averages.aspx

A moving average that also takes into account the previous price information of the underlying currency.

An exponentially smoothed moving average is a weighted moving average in which the weight factors are powers of S, the smoothing constant. An exponentially smoothed moving average is computed over all the data accumulated so far instead of being chopped off after some number of days. For day d the exponentially smoothed moving average is: A_d = \frac{\sum_{i=1}^{d} S^{i-1} M_{(d-i)+1}}{\sum_{i=1}^{d} S^{i-1}} But this is just a geometric sequence! The next term in such a sequence is given by: Ad=(1-S)Md+SAd-1. Calculation is expedited and comprehension served if we substitute: P=1-S for S into the equation for the next term. Doing a little algebra, we discover: A[d] = A[d - 1] + P (M[d] - A[d - 1]) This reformulation makes the operation of smoothing very intuitive. Every day, we take the old trend number Ad-1, calculate the difference between it and today's measurement Md, then add a percentage of that difference P to the old trend value obtain the new one. Obviously, the closer P

Exponential smoothing is a technique that can be applied to time series data, either to produce smoothed data for presentation, or to make forecasts. The time series data themselves are a sequence of observations. The observed phenomenon may be an essentially random process, or it may be an orderly, but noisy, process. Whereas in the simple moving average the past observations are weighted equally, exponential smoothing assigns exponentially decreasing weights over time.