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Weighted Moving Average

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A weighted average is any average that has multiplying factors to give different weights to different data points. But in technical analysis a weighted moving average (WMA) has the specific meaning of weights which decrease arithmetically. In an n-day WMA the latest day has weight n, the second latest n-1, etc, down to zero.

When calculating the WMA across successive values, it can be noted an amount p2 to pn + 1 drops out of the numerator each day. The WMA can thus be calculated starting with the above formula but then stepping successively with just additions and subtractions, not a full set of multiplications,

Totaltoday = Totalyeseterday + p1pn + 1


Numerator
today = Numeratoryesterday + np1Totalyesterday


The denominator, incidentally, is a triangle number, and equals n(n+1)\over2

The graph below shows how the weights decrease, from highest weight for the most recent days, down to zero. It can be compared to the weights in the exponential moving average which follows.


WMA weights N=15

Parameters

  • Period (9) - The number of bars in a chart. If the chart displays daily data, then period denotes days; in weekly charts, the period will stand for weeks, and so on.

Interpretation

Since a Weighted Moving Average assigns more importance to recent price values, it is more sensitive to price activity than the Simple Moving Average. The Weighted Moving Average tends to stick closer to the trend. Analysts use the Weighted Moving Average in the same manner and for the same purposes as the other Moving Averages, although the advantage of the Weighted Moving Average is that it provides stronger and earlier indications to trend direction and reversal because it focuses on the more recent price data.


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