Moving Average
The Moving Average Technical Indicator shows the mean instrument price
value for a certain period of time. When one calculates the moving average,
one averages out the instrument price for this time period. As the price
changes, its moving average either increases, or decreases.
There are four different types of moving averages: Simple (also referred to as
Arithmetic), Exponential, Smoothed and Linear
Weighted. Moving averages
may be calculated for any sequential data set, including opening and closing
prices, highest and lowest prices, trading volume or any other indicators. It is
often the case when double moving averages are used.
The only thing where moving averages of different types diverge considerably
from each other, is when weight coefficients, which are assigned to the latest
data, are different. In case we are talking of simple moving average, all prices
of the time period in question, are equal in value. Exponential and Linear
Weighted Moving Averages attach more value to the latest prices.
The most common way to interpreting the price moving average is to
compare its dynamics to the price action. When the instrument price rises
above its moving average, a buy signal appears, if the price falls below its
moving average, what we have is a sell signal.
This trading system, which is based on the moving average, is not designed
to provide entrance into the market right in its lowest point, and its exit right
on the peak. It allows to act according to the following trend: to buy soon after
the prices reach the bottom, and to sell soon after the prices have reached
their peak.
Moving averages may also be applied to indicators. That is where the
interpretation of indicator moving averages is similar to the interpretation of
price moving averages: if the indicator rises above its moving average, that
means that the ascending indicator movement is likely to continue: if the
indicator falls below its moving average, this means that it is likely to continue
going downward.
Here are the types of moving averages on the chart:
- Simple Moving Average (SMA)
- Exponential Moving Average (EMA)
- Smoothed Moving Average (SMMA)
- Linear Weighted Moving Average (LWMA)
Calculation:Simple Moving Average (SMA)
Simple, in other words, arithmetical moving average is calculated by summing
up the prices of instrument closure over a certain number of single periods
(for instance, 12 hours). This value is then divided by the number of such
periods.
SMA = SUM(CLOSE, N) / N
Where:
N — is the number of calculation periods.
Exponential Moving Average (EMA)
Exponentially smoothed moving average is calculated by adding the moving
average of a certain share of the current closing price to the previous value.
With exponentially smoothed moving averages, the latest prices are of more
value. P-percent exponential moving average will look like:
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)
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:
PREVSUM = SMMA(i - 1) * N
SMMA(i) = (PREVSUM - SMMA(i - 1) + CLOSE(i)) / N
Where:
SUM1 — is the total sum of closing prices for N periods;
PREVSUM — smoothed sum of previous bar;
SMMA1 — is the smoothed moving average of the first bar;
SMMA(i) — is the smoothed moving average of the current bar (except for
the first one);
CLOSE(i) — is the current closing price;
N — is the smoothing period.
The formula can be simplified as a result of arithmetic manipulations:
SMMA (i) = (SMMA(i - 1) * (N - 1) + CLOSE (i)) / N
Linear Weighted Moving Average (LWMA)
In the case of weighted moving average, the latest data is of more value than
more early data. Weighted moving average is calculated by multiplying each
one of the closing prices within the considered series, by a certain weight
coefficient.
LWMA = SUM(Close(i)*i, N) / SUM(i, N)
Where:
SUM(i, N) — is the total sum of weight coefficients.