Exponential Moving Average (EMA)

Although SMA is an excellent tool, one major problem is associated with it: SMA is very sensitive to sudden jumps (spikes). By looking at the next example you will better understand what I mean:
Suppose that we draw a 5 SMA on the daily chart of EUR / USD and the closing prices for the last 5 days are as follows: 1st day - 1.2345, 2nd day - 1.2350, 3rd day - 1.2360, 4th day - 1.2365, 5th day - 1.2370. SMA would be calculated as: (1.2345+1.2350+1.2360+1.2365+1.2370)/5 = 1.2358. But what if the 2nd day price was 1.2300? SMA result would be much lower and you get the impression that the price is going down, when in reality, 2nd day may perhaps have been only one remote event (for example, reduction of the interest rate).

What I am trying to indicate is that the SMA may sometimes be too simple. If there was only a way to filter the jumps so that we do not get the wrong picture and make the most out of moving averages. It exists and is called the Exponential Moving Average (EMA).

EMA is a type of moving average that is similar to Simple Moving Average, except that more weight is given to the latest data. The Exponential Moving Average is also known as "Exponentially Weighted Moving Average". This type of moving average reacts faster to recent price changes than a Simple Moving Average. In our example above, EMA would put more weight on the 3rd-5th day, which means that jump on the 2nd would have a lesser value and would not influence so much on the moving average. It would put more emphasis on what traders are doing right now. While trading, it is more important to see what merchants are doing right now, not what they were doing last week or last month.



EMA = (CLOSE(i)*P)+(EMA(i-1)*(100-P)) ; Where:
CLOSE(i) = the price of the current period closure
EMA(i-1) = Exponentially Moving Average of the previous period closure
P = the percentage of using the price value

Smoothed Moving Average (SMMA)

A Smoothed Moving Average is sort of a cross between a Simple Moving Average and an Exponential Moving Average, only with a longer period applied. The Smoothed Moving Average gives the recent prices an equal weighting to the historic ones. The calculation does not refer to a fixed period, but rather takes all available data series into account. This is achieved by subtracting yesterday’s Smoothed Moving Average from today’s price. Adding this result to yesterday’s Smoothed Moving Average, results in today’s moving average.

In a Simple Moving Average, the price data have an equal weight in the computation of the average. Also, in a Simple Moving Average, the oldest price data are removed from the moving average as a new price is added to the computation. The Smoothed Moving Average uses a longer period to determine the average, assigning a weight to the price data as the average is calculated. Thus, the oldest price data points in the Smoothed Moving Average are never removed, but they have only a minimal impact on the moving average, which is similar to how an Exponential Moving Average places more weight on the more recent data.

The first value of this smoothed moving average is calculated as the simple moving average (SMA):
SUM1 = SUM(CLOSE, N)
SMMA1 = SUM1/N

The second and succeeding moving averages are calculated according to this formula:
SMMA(i) = (SUM1-SMMA1+CLOSE(i))/N ; Where:
SUM1 = the total sum of closing prices for N periods
SMMA1 = the smoothed moving average of the first bar
SMMA(i) = the smoothed moving average of the current bar (except for the first one)
CLOSE(i) = the current closing price
N = the smoothing period