A weighted average is more heavily influenced by some of the numbers it is calculated from than others.
It is calculated by:
- multiplying each number by a weight
- adding the results together
- dividing the total by the sum of the weights.
A useful weighted average for time series data (common in finance and economics) is and exponential one:
St = αxt + (1 - α)St - 1, and
S0 = x0
where S is the exponentially weighted average, or smoothed value
x is the series being averaged,
subscripts denote time, with the first period being 0, and
0 < α < 1
This gives weightings to xt, xt - 1, xt - 2, etc. in proportions 1, (1 - α), (1 - α)2, etc.
When this is used to produce a new time series (often to draw a graph), when it is called exponential smoothing.