## Python numpy moving average for data

The following examples produces a moving average of the preceding WINDOW values. We truncate the first (WINDOW -1) values since we can’t find the average before them. (The default behaviour for convolution is to assume that values before the start of our sequence are 0). (More formally, we construct the sequence y for the sequence x where y_i = (x_i + x_(i+1) + …. x_(i+n)) / n)

```WINDOW = 10
data = [1,2,3,4,5,5,5,5,5,5,5,5,5,5,5]
weightings = numpy.repeat(1.0, WINDOW) / WINDOW
numpy.convolve(data, weightings)[WINDOW-1:-(WINDOW-1)]
```

This makes use of numpy’s convolution function. This is a general purpose moving average operation.

Changing weightings makes some values more important; offsetting appropriately allows you to view average as around point rather than before point.

Rather than truncating values we can fix the initial values in place, as illustrated in this example:

```WINDOW = 10
data = [1,2,3,4,5,5,5,5,5,5,5,5,5,5,5]
extended_data = numpy.hstack([[data[0]] * (WINDOW- 1), data])
weightings = numpy.repeat(1.0, WINDOW) / WINDOW
numpy.convolve(extended_data, weightings)[WINDOW-1:-(WINDOW-1)]
```

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• 1. Christian  |  April 26, 2011 at 4:47 pm

Thanks for the tip, I found it useful!

You have a slight error in your fixed initial value example: “extended_data” should be the one being convolved, not “data”.

• 2. Anon  |  April 26, 2011 at 6:20 pm

Thanks for spotting that! I’ve amended the example.

• 3. Greg Haskins  |  June 16, 2011 at 12:03 am

Nice tip, thanks. I knew there had to be an optimized way for numpy to compute rolling averages.

From the docs (http://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html), it looks like your recipe could be even more concise by using the mode=”valid” keyword instead of slicing:

>>> WINDOW = 10
>>> data = [1,2,3,4,5,5,5,5,5,5,5,5,5,5,5]
>>> weightings = numpy.repeat(1.0, WINDOW) / WINDOW
>>> numpy.convolve(data, weightings)[WINDOW-1:-(WINDOW-1)]
array([ 4. , 4.4, 4.7, 4.9, 5. , 5. ])
>>> numpy.convolve(data, weightings, ‘valid’)
array([ 4. , 4.4, 4.7, 4.9, 5. , 5. ])

• 4. Simple moving average and the swiss franc « quantathoughts  |  September 11, 2011 at 4:37 pm

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• 5. daFeda  |  September 11, 2012 at 10:36 am

Very useful, thank you.