The theory behind a Weighted Moving Average (WMA) is that the recent data is more relevant than past data. Therefore, it puts more "weight" on the recent data and less weight on the older data.
To calculate it, take the number of periods to be analyzed and invert the number of interval remaining into the weighting for each interval's price. Once a weighting has been established for each interval, multiply the price for that interval by its weighting factor. Finally, add up all the weighted prices and then divide the sum of the weighted prices by the sum of the weightings. The result will be the average weighted price for the interval.
The following table shows the calculation of a 4day weighted moving average:
Day No  Weighting  Price 
 Weighted  Average 
1  4 X  $ 20.15  =  $ 80.60 

2  3 X  $ 19.95  =  $ 59.85 

3  2 X  $ 19.20  =  $ 38.40 

4  1 X  $ 18.95  =  $ 18.95 

  

    
Totals  10  $ 197.80 / 10 =  $ 19.78 
The user can alter two inputs (Period and Data Field) as well as control the visual display of the line from the Mov Avg  Weighted Properties dialog box.
The user can set the number of previous intervals that will be averaged with the current interval to produce the weighted average for a given interval.
Type in a whole number in the Periods text box in the Parameters tab of the Mov Avg  Weighted Properties dialog box.
Most traders prefer to calculate the weighted average using the Close data field. This is the default setting. However it is possible to choose other data fields from the dropdown list, the choices include: Open, High, Low, Close, Bid, Ask, Volume and Open Interest.
The weighted moving average plot is a line superimposed over the price chart.
The exact display of the plot is controlled on the Plots tabbed page of the Mov Avg  Weighted Properties dialog box.
The Style selected for the line plot can be one of the following: Solid, Dashes, Dots, and Points.
Once the style is selected, each lines Color and Weighting are also controlled from this page.
The Scale's display is controlled from the Scale Settings and Scale Appearance tabbed pages.
A weighted moving average will more quickly respond to price changes than a simple moving average will:
In this example, the weighted moving average line (dark blue) responds more rapidly to the reversals in the price chart, even though it uses the same 10 intervals of close prices as the simple moving line (teal green) does.
Two other indicators can be used to reduce noise or change the bias in favor of more recent data.
Short period moving averages can sometimes be plotted so close to the price chart that numerous false signals are generated. The easiest way remove this noise is to move the plot of the simple moving average a few intervals forward, this will delay signals from the indicator and remove noise.
For long time periods, the moving average plotted for a particular interval is actually lagging because it is composed of past data. By moving the plot backward half the number of periods on which the average is calculated, the plot can be "centered" over the current interval and be more statistically correct.
The displaced moving average (Mov Avg  Displaced) indicator has a setting to accomplish both of these objectives.
Another indicator that alters the calculation itself, similar to the weighting calculation of the Mov Avg  Weighted, is the exponential moving averages (Mov Avg  Exponential).
The following chart compares both weighted and exponential moving averages with the simple moving average:
The simple moving average (blue dotted line) gives equal weight to all data from its 20 interval calculation period.
The exponential (solid purple line) and weighted (solid yellow line) each use a different calculation to give greater importance to more recent data. For this reason both lines more closely track the current price chart, but the each method of calculation causes them to be slightly different.