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MovingAverage

✖
MovingAverage[list,r]

gives the moving average of list, computed by averaging runs of r elements.

✖
MovingAverage[list,{w1,w2,…,wr}]

gives the moving average of list, computed with weights wi.

Details

Examples

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Basic Examples  (2)Summary of the most common use cases

Compute a pairwise simple moving average:

In[1]:=1
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https://wolfram.com/xid/0fq33uh1qn7a8-d3rle3
Out[1]=1

Compute weighted moving averages:

In[1]:=1
✖
https://wolfram.com/xid/0fq33uh1qn7a8-g33se6
Out[1]=1

Scope  (5)Survey of the scope of standard use cases

Lists of integers yield rational numbers:

In[1]:=1
✖
https://wolfram.com/xid/0fq33uh1qn7a8-nib
Out[1]=1

Lists of approximate numbers yield approximate numbers:

In[2]:=2
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https://wolfram.com/xid/0fq33uh1qn7a8-blyosq
Out[2]=2

Moving averages of matrices are matrices:

In[1]:=1
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https://wolfram.com/xid/0fq33uh1qn7a8-f6w30t
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq33uh1qn7a8-hrjjx3
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq33uh1qn7a8-k2qtt9
Out[3]=3

Obtain results for lists of any precision:

In[1]:=1
✖
https://wolfram.com/xid/0fq33uh1qn7a8-dftm52
Out[1]=1

Obtain results for weights of any precision:

In[1]:=1
✖
https://wolfram.com/xid/0fq33uh1qn7a8-e6ou1d
Out[1]=1

Filter large datasets:

In[1]:=1
✖
https://wolfram.com/xid/0fq33uh1qn7a8-jgjmh7
In[2]:=2
✖
https://wolfram.com/xid/0fq33uh1qn7a8-cm87ky
In[3]:=3
✖
https://wolfram.com/xid/0fq33uh1qn7a8-crc6al
Out[3]=3

Generalizations & Extensions  (4)Generalized and extended use cases

Compute results for a SparseArray:

In[1]:=1
✖
https://wolfram.com/xid/0fq33uh1qn7a8-l4ct3
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq33uh1qn7a8-d6csj0
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq33uh1qn7a8-d4vr8
Out[3]=3

A moving average of TemporalData places the result on the right end of the moving windows:

In[1]:=1
✖
https://wolfram.com/xid/0fq33uh1qn7a8-kwktnd
Out[1]=1

Incomplete windows are dropped:

In[2]:=2
✖
https://wolfram.com/xid/0fq33uh1qn7a8-bjys8
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq33uh1qn7a8-zv8bvv
Out[3]=3

The values of a moving average of TemporalData are equivalent to the moving average of its values:

In[1]:=1
✖
https://wolfram.com/xid/0fq33uh1qn7a8-9somgq
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq33uh1qn7a8-1jfxow
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq33uh1qn7a8-1zebv8
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0fq33uh1qn7a8-3bcldd
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/0fq33uh1qn7a8-k1n3kb
Out[5]=5

The results of a moving average of TemporalData are placed on the right end of the window, and the windows with the smaller number of observations then requested are dropped:

In[6]:=6
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https://wolfram.com/xid/0fq33uh1qn7a8-t5qtkt
Out[6]=6
In[7]:=7
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https://wolfram.com/xid/0fq33uh1qn7a8-ln31xf
Out[7]=7

The moving average of a numeric TimeSeries for various window lengths:

In[1]:=1
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https://wolfram.com/xid/0fq33uh1qn7a8-i7bgj9
In[2]:=2
✖
https://wolfram.com/xid/0fq33uh1qn7a8-q7g8c4
In[3]:=3
✖
https://wolfram.com/xid/0fq33uh1qn7a8-euuy8l

Incomplete windows are dropped, and the result is placed on the right end of each window:

In[4]:=4
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https://wolfram.com/xid/0fq33uh1qn7a8-z7py9p
In[5]:=5
✖
https://wolfram.com/xid/0fq33uh1qn7a8-fa5nzt
Out[5]=5

Applications  (2)Sample problems that can be solved with this function

Smooth noisy data:

In[1]:=1
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https://wolfram.com/xid/0fq33uh1qn7a8-j42qsa
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq33uh1qn7a8-biof3w
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq33uh1qn7a8-wjb0f
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0fq33uh1qn7a8-czj2v8
Out[4]=4

Compute the 100-day moving average of a financial time series:

In[1]:=1
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https://wolfram.com/xid/0fq33uh1qn7a8-ur987c
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq33uh1qn7a8-cq2lfi
Out[2]=2

Properties & Relations  (7)Properties of the function, and connections to other functions

A moving average is a sequence of means:

In[1]:=1
✖
https://wolfram.com/xid/0fq33uh1qn7a8-bxc2b1
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq33uh1qn7a8-i0fg4m
Out[2]=2

A two‐term MovingAverage is equivalent to a two‐term MovingMedian:

In[1]:=1
✖
https://wolfram.com/xid/0fq33uh1qn7a8-i96jjd
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq33uh1qn7a8-1z6z5
Out[2]=2

MovingAverage is equivalent to MovingMap of Mean:

In[1]:=1
✖
https://wolfram.com/xid/0fq33uh1qn7a8-bcf2i7
In[2]:=2
✖
https://wolfram.com/xid/0fq33uh1qn7a8-banxzo
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq33uh1qn7a8-dm1j4i
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0fq33uh1qn7a8-ej6qwp
Out[4]=4

An n‐term moving average is equivalent to a moving average with n equal weights:

In[1]:=1
✖
https://wolfram.com/xid/0fq33uh1qn7a8-bht95i
In[2]:=2
✖
https://wolfram.com/xid/0fq33uh1qn7a8-j2233w
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq33uh1qn7a8-slsqb
Out[3]=3

An n‐term moving average is equivalent to a ListCorrelate:

In[1]:=1
✖
https://wolfram.com/xid/0fq33uh1qn7a8-cv4c5m
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq33uh1qn7a8-fynz0w
Out[2]=2

An n‐term weighted moving average is equivalent to a ListCorrelate:

In[1]:=1
✖
https://wolfram.com/xid/0fq33uh1qn7a8-joj1hm
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0fq33uh1qn7a8-hh3b5j
Out[2]=2

Multiplying weights by a constant gives the same moving average:

In[1]:=1
✖
https://wolfram.com/xid/0fq33uh1qn7a8-c0225r
In[2]:=2
✖
https://wolfram.com/xid/0fq33uh1qn7a8-d3zciv
Out[2]=2
Wolfram Research (2007), MovingAverage, Wolfram Language function, https://reference.wolfram.com/language/ref/MovingAverage.html.
✖
Wolfram Research (2007), MovingAverage, Wolfram Language function, https://reference.wolfram.com/language/ref/MovingAverage.html.

Text

Wolfram Research (2007), MovingAverage, Wolfram Language function, https://reference.wolfram.com/language/ref/MovingAverage.html.

✖
Wolfram Research (2007), MovingAverage, Wolfram Language function, https://reference.wolfram.com/language/ref/MovingAverage.html.

CMS

Wolfram Language. 2007. "MovingAverage." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MovingAverage.html.

✖
Wolfram Language. 2007. "MovingAverage." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MovingAverage.html.

APA

Wolfram Language. (2007). MovingAverage. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MovingAverage.html

✖
Wolfram Language. (2007). MovingAverage. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MovingAverage.html

BibTeX

@misc{reference.wolfram_2025_movingaverage, author="Wolfram Research", title="{MovingAverage}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/MovingAverage.html}", note=[Accessed: 12-May-2025 ]}

✖
@misc{reference.wolfram_2025_movingaverage, author="Wolfram Research", title="{MovingAverage}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/MovingAverage.html}", note=[Accessed: 12-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_movingaverage, organization={Wolfram Research}, title={MovingAverage}, year={2007}, url={https://reference.wolfram.com/language/ref/MovingAverage.html}, note=[Accessed: 12-May-2025 ]}

✖
@online{reference.wolfram_2025_movingaverage, organization={Wolfram Research}, title={MovingAverage}, year={2007}, url={https://reference.wolfram.com/language/ref/MovingAverage.html}, note=[Accessed: 12-May-2025 ]}