Weighted MA

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Moving averages are considered to be one of the basic and most important indicators in technical analysis. They are analyzed alone as well as used as components in many other technical studies. Two of the most important types of moving average are the Simple Moving Average (SMA) and the Exponential Moving Average (EMA). These averages are used to show the mean of prices during a certain number of previous time periods (previous price-bars) and to smooth short-time price volatility.

The common problem with moving averages is the lag between price movements and a moving average's trend. The longer the bar period is that you select, the smoother is the moving average and the better is the filtration of volatile price spikes. However, the longer the bar period setting, the greater will be the lag and the later your signals will be generated. Different methods have been created to reduce the lag by keeping the smoothing at desirable level. One of the methods to reduce lag is to use a weighted moving average that uses a weighted coefficient for each price period (price bar) that is used in the calculation.

Weighted Moving averages are used in the same way as are the SMA and EMA. If the price rises above the WMA, the price trend is considered to be bullish and when the price falls below the WMA, the price trend is considered to be bearish. In a similar way, two WMAs with different bar period settings could be used to define a trend as well as generate signals.

Chart 1: NASDAQ 100 Chart - Simple and Weighted Moving Averages
(bar period setting = 30 for both MA)



As a rule the price moving averages are used to confirm trends, resistance and support levels as  one of the components of different trading systems. It is recommended price moving averages be used in conjunction with other technical indicators. Using moving averages as part of a trading system to confirm other indicators can greatly enhance this trading system.

Formula and Calculations

A Weighed Moving Average (WMA) emphasizes the importance of the most recent price and is calculated by the following formula:

WMA(N) = [ ( N*P0 + (N-1)*P1 + (N-2)*P2 + ... + PN ) ] / (1 + 2 + 3 + ... + N)

where:

WMA(N) = the Weighted Moving Average over N price-bars.
N = the bar period setting (number of bars used in calculation)
P0 = the price of the last bar
P1 = the price of the previous bar
PN = the price of the last bar in the sequence
(1 + 2 + 3 + ... + N) could be calculated by using following simpler formula:
(1 + 2 + 3 + ... + N) = N*(N+1)/2