Moving Average/Basic Approach

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Generic Approach to Moving Average

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An element moves in an additive Group (mathematics) or Vector Space V. In a generic approach, we have a moving probability distribution that defines how the values in the environment of have an impact on the moving average.

Discrete/continuous Moving Average

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According to probability distributions we have to distinguish between a

  • discrete (probability mass function ) and
  • continuous (probability density function )

moving average. The terminology refers to probability distributions and the semantics of probability mass/density function describes the distrubtion of weights around the value . In the discrete setting the means that has a 20% impact on the moving average for .

Moving/Shift Distributions

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If the probility distribution are shifted by in . This means that the probability mass functions resp. probability density functions are generated by a probability distribution at the zero element of the additive group resp. zero vector of the vector space. Due to nature of the collected data f(x) exists for a subset . In many cases T are the points in time for which data is collected. The and the shift of a distribution is defined by the following property:

  • discrete: For all the probability mass function fulfills for
  • continuous: For all probability density function fulfills

The moving average is defined by:

  • discrete: (probability mass function )

Remark: for a countable subset of

  • continuous probability density function

It is important for the definition of probability mass functions resp. probability density functions that the support (measure theory) of is a subset of T. This assures that 100% of the probability mass is assigned to collected data. The support is defined as: