Weighted Moving Average Function

A Weighted Moving Average Function is a moving average function that uses a weighted average function (to report a weighted average value for the k last series values).

• Context:
  • It can be referenced by a Moving Average-based Forecasting System (that implements a moving average-based forecasting algorithm).
• Example(s):
  • an Exponentially Weighted Moving Average/Exponential Moving Average.
  • …
• Counter-Example(s):
  • a Simple Moving Average.
  • a Kalman Filter.
  • an Autoregressive Integrated Moving Average Function.
• See: Time Series Analysis, Non-Parametric Statistical Model, Moving Average Function, Weighted Function, Exponential Smoothing.

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References

2016

• (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/exponential_smoothing#The_weighted_moving_average Retrieved:2016-8-31.
  • A slightly more intricate method for smoothing a raw time series {x_t} is to calculate a weighted moving average by first choosing a set of weighting factors : [math]\displaystyle{ \lbrace w_1, w_2,\dots,w_k \rbrace }[/math] such that [math]\displaystyle{ \sum_{n=1}^k w_n = 1 }[/math] and then using these weights to calculate the smoothed statistics {s_t}: : [math]\displaystyle{ s_t = \sum_{n=1}^k w_n x_{t+1-n} = w_1x_t + w_2x_{t-1} + \cdots + w_kx_{t-k+1}. }[/math] In practice the weighting factors are often chosen to give more weight to the most recent terms in the time series and less weight to older data. Notice that this technique has the same disadvantage as the simple moving average technique (i.e., it cannot be used until at least k observations have been made), and that it entails a more complicated calculation at each step of the smoothing procedure. In addition to this disadvantage, if the data from each stage of the averaging is not available for analysis, it may be difficult if not impossible to reconstruct a changing signal accurately (because older samples may be given less weight). If the number of stages missed is known however, the weighting of values in the average can be adjusted to give equal weight to all missed samples to avoid this issue.

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