Averages can be placed through the high and low. When prices close beyond both lines a trend may start. Exits can be taken when the price closes back beyond the previous average.

The CQG Moving Average study plots the average price over a user-specified period in bars. Five methods of calculating the Moving Average are available in CQG/Windows - Simple, Smoothed, Centered, Weighted and Exponential.

Simple:

For the following example the PERIOD equals 3.

The first value for a Simple Average is determined by formula SIMPLE. It is plotted on the chart at the third bar from the left side of the screen.

SIMPLE = (PRICE 1 + PRICE 2 + PRICE 3)/PERIOD

The next value would be plotted at the fourth bar from the left side of the screen.

SIMPLE = (PRICE 2 + PRICE 3 + PRICE 4)/PERIOD

Eliminating the oldest PRICE from the calculation, and including the next more recent PRICE, determines subsequent values.

Smooth:

A Smoothed Moving Average is similar to a simple moving average. However, in a smoothed moving average, rather than subtracting the oldest value the previous smoothed average value is subtracted.

For the following example the PERIOD equals 3.

The first value for a Smoothed Moving Average is determined by the formula SMOOTH. It is plotted on the chart at the third bar from the left side of the screen.

SMOOTH =(PRICE 1 + PRICE 2 + PRICE 3)/PERIOD

The next value would be plotted at the fourth bar from the left side of the screen.

SMOOTH2 = (PREVIOUS SUM - PREVIOUS AVG + PRICE 4)/PERIOD

For the second calculation of SMOOTH, PREVIOUS SUM is the sum of PRICE 1 + PRICE 2 + PRICE 3; and PREVIOUS AVG is the initial value of SMOOTH.

The next value would be plotted at the fifth bar from the left side of the screen. SMOOTH = (PREVIOUS SUM - PREVIOUS AVG + PRICE 5)/PERIOD. Subsequent values would be determined by subtracting the PREVIOUS AVG from the PREVIOUS SUM, adding the next more recent PRICE, then dividing by the PERIOD.

Example: If the values 1,2,3,4 and 5 were reported for the first five bars the three-period smoothed moving averages for those bars would be calculated as follows:

Centered:

A Centered Average is calculated the same as a Simple Average - the difference is where the first point is plotted. A Centered Average plots the first point at the center bar of the specified PERIOD.

For example: The first point for a 3 PERIOD Centered Average would be plotted at the second Bar, where the first point for a 3 PERIOD Simple or Smoothed average would be plotted at the third Bar.

In the case of a Centered Average with an even number of PERIODs, the first point would be plotted at the bar immediately to the right of the center bar.

Weighted:

According to Technical Analysis from A to Z, by Steven Achelis, "A weighted moving average is designed to put more weight on recent data and less weight on past data. A weighted moving average is calculated by multiplying each of the previous day's data by a weight. The weight is based on the number of days in the moving average."

In the above example, the weight of the fifth day is one, while the weight value on the most recent day is five. This gives five times more weight to today's price than the price five days ago.

The price value for the fifth day (from the current price value) is multiplied by one, the fourth day by two, the third day by three, the second day by four, and the current day by five, in a five-period weighted moving average. This sum is then divided by the total of the weight multipliers (1+2+3+4+5, or 15).

Formula for a Weighted Moving Average:
((Close(@)[-4]*1(Close(@)[-3]*2)+(Close(@)[-2]*3)+(Close(@)[-1]*4)+(Close (@)*5))/15

Exponential:

For the following example the PERIOD equals 3 and the PRICE equals CLOSE.

To calculate an Exponentially Smoothed Moving Average (ESMA) the user must enter an integer value for the PERIOD or a decimal value Smoothing Constant.

A decimal value Smoothing Constant must be greater than 0.0 and less than or equal to 2.0. Example: .5

When an integer value is entered for PERIOD it is converted by the system to a decimal value Smoothing Constant using the following formula:

The ESMA may be calculated after the Smoothing Constant is known. The first ESMA value is initially set to the first PRICE before the calculation begins. The first PRICE is from the left-most bar on the screen.

The formula for calculating the ESMA is as follows:

ESMA = pESMA - (-Smoothing Constant X ( pESMA - PRICE ) )

In the above formula:

ESMA is the new Exponentially Smoothed Moving Average.

pESMA is the Previous ESMA value.

PRICE is the value of the PRICE used for each bar, e.g. CLOSE

Note: A decimal value Smoothing Constant equal to 0.0 stops the ESMA from being displayed, however, an ESMA will appear if the integer 0 is entered without the decimal point.

CQG/Windows also provides the ability to add Envelopes to a MA. These lines are added to a MA when a figure is entered under PERCENT. The envelopes are equal to the MA times one plus the percent and one minus the percent.

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