Information & Articles Product guide Trading IQ Game with great prizes Support  Home  Site Map  Testimonials 
The new Member FORUM is completed and you can earn up to $200 in credits by posting and leaving feedback
What is a weighted moving average and how is it calculated? 

Weighted moving average explanation with chart examples and formula
Weighted average of world population from 1982 to 2010
You can see the world population data below together with the alarming growth rate. Below it is the 4 period weighted moving average of it.
The colour coding is used to show how the calculations are made. The first four periods are 4.59, 4.75, 4.92, 5.09 now we will look at the calculation.
It is more complex than the calculation of the simple moving average as it "weights" more on the most recent data and "fades" the older data.
The calculation is shown below.
Period 1 (4.59 x 1 ) + Period 2 (4.75 x 2) + Period 3 (4.92 x 3) + Period 4 ( 5.09 x 4) = 49.21 then we divide this by the sum of the data x multiplier. Which is 1+2+3+4 = 10 which gives us 4.92 as a four period weighted average.
So to explain what is happening I will start at the beginning. The first period used is always = to itself which is the same as multiplied by 1. The second period is multiplied by 2 The third period is multiplied by 3 The fourth period is multiplied by 4.
Once we have them multiplied up, we add all the multiplier used up together thus 1 + 2 +3 +4 = 10. So the number 10 will be our divisor which we use to divide the total of Period1 x 1 + Period2 x 2 + Period 3 x 3 + Period 4 x 4.
The correct mathematic statement for this would be ( (4.59 x 1 ) + (4.75 x 2) + (4.92 x 3) ( 5.09 x 4)) / 10 Please note there are double brackets around the formula above. Basically this means you will do the small calculations first and then the final division by 10 is the last step.
The next stage in creating a weighted moving average is to roll forward to the right by 1 number. So for the next value we will use Period 2 ,3, 4, 5, 6
Key points to remember
In the next example we shall use a 6 period weighted moving average.
Weighted average of USA unemployment figures from 1998 to 2012
As before we are going to start by multiplying period 1 by 1 and then move across from left to right adding 1 to the multiplier in each step. Thus...
Period 1 (4.50 x 1 ) + Period 2 (4.20 x 2) + Period 3 (3.90 x 3) + Period 4 (4.6 x 4) + Period 5 ( 5.8 x 5 ) + Period 6 ( 6.2 x 6 ) = 109.2 then we divide this by the summation of all multipliers. Which is 1+2+3+4+5+6 = 21 which gives us 5.20 as a six period weighted average.
The calculation is then shifted one data point to the right so for the 2nd value we use the following...remembering that the first value is multiplied by 1.
Period 2 (4.20 x 1 ) + Period 3 (3.90 x 2 ) + Period 4 (4.6 x 3 ) + Period 5 ( 5.8 x 4 ) + Period 6 ( 6.2 x 5 ) +Period 7( 5.4 x 6) = 112.40
Again we divide this by he total of all the multipliers which is 1+2+3+4+5+6 = 21 which gives us 112.40 divided by 21 = 5.35.
Mathematical symbol for weighted average
Other types of moving average and formulas


PLA Dynamical is the fastest moving average on the planet ( If overshoot = True and Speed = 100) 



PLA Dynamical response times compared to standard type MA type filters Tested at length 30



Precision Trading Systems is provider of the following 
Introduction 
Precision Trading Systems is partnered with MultiCharts.
Precision Trading Systems is part of the NinjaTrader ecosystem.
Systems and Indicators for Tradestation, NinjaTrader and MultiCharts.
Top quality paid & FREE trading systems and indicators for most platforms
Members can receive some paid products completely FREE
Roger Medcalf is a vendor on the Tradestation App store
Roger Medcalf is a vendor of products of MetaTrader 4
Free to play Trading IQ Game with generous PRIZES from our sponsors.

RISK
DISCLOSURE

Futures, Forex and Stock trading contain substantial risk and are
not for every investor.

An
investor could potentially lose all or more of the initial
investment.

Risk
capital is money that can be lost without jeopardizing ones
financial security or lifestyle.

Only
risk capital should be used for trading

Only
those with sufficient risk capital should consider trading.

Past
performance is not necessarily indicative of future results.
HYPOTHETICAL PERFORMANCE
DISCLOSURE
Hypothetical performance results have
many inherent limitations, some of which are described below. no
representation is being made that any account will or is likely to
achieve profits or losses similar to those shown; in fact, there are
frequently sharp differences between hypothetical performance results
and the actual results subsequently achieved by any particular trading
program. One of the limitations of hypothetical performance results is
that they are generally prepared with the benefit of hindsight. In
addition, hypothetical trading does not involve financial risk, and no
hypothetical trading record can completely account for the impact of
financial risk of actual trading. for example, the ability to withstand
losses or to adhere to a particular trading program in spite of trading
losses are material points which can also adversely affect actual
trading results. There are numerous other factors related to the markets
in general or to the implementation of any specific trading program
which cannot be fully accounted for in the preparation of hypothetical
performance results and all which can adversely affect trading results.