Weighted Moving Average

What

The Weighted Moving Average WMA is measured by averaging all the previous values over the given period, (also the ongoing value). These values are weighted linearly (the oldest value gets a weight of 1, the next value gets a weight of 2, and so on up to the ongoing value, which gets the same weight as the period). Until there are enough values to fill the given period the moving average at the start of a data series is not determined.

It's important to remember that for more exaggerated weighting on the ongoing values, you may use an EMA. You could also average 2 or more WMA together.

Moving averages can be used to see trends, that's why they can also be used to predict if data is bucking the trend. A weighted moving average is measured by multiplying each of the previous day's data by a weight. The weight in its turn is based on the number of days in the moving average. For example, the first day's weight is 1.0 while the value on the most recent day is 5.0. This gives 5 times more weight to today's price than the price 5 days before.

How

The weighted moving average is calculated by multiplying each datum in your series by a different ratio and then taking the sum of those products. Because of the complexity of calculating this moving average, an example follows.

Assume the closing prices over the last 5 days are:

Day          1              2              3              4              5 (current) 

Price        77            79            79            81            83 

The formula for the ratio that is applied to each of the prices is:

‘N’, the numerator in each case is the numeral of the day number in the series.

‘D’, the denominator is the sum of the number of days as a triangular number. Since there are 5 days, the triangular numbers are 5, 4, 3, 2, and 1. The sum is 5+4+3+2+1=15. 

Therefore the 5 Day WMA is 83(5/15) + 81(4/15) + 79(3/15) + 79(2/15) + 77(1/15) = 80.7

Day          1              2              3              4              5 (current) 

Price        77            79            79            81            83 

WMA                                                                       80.7 

When

WMA can be used with the same theory as all other moving averages, that is levels are interpreted as support in a rising market, or resistance in a falling market. Traders can buy when the market price breaks up through the moving average and sell when the market price breaks down through the moving average. The difference between the SMA and WMA can be viewed below. The WMA is coloured blue and the SMA is coloured red. Using an EMA opposed to an SMA will give you a reading with less lag & will be more tightly tracked to the price.