[Python] Weighted moving average with numpy.convolve

I'm writing a moving average (MA) function that uses the convolve function in NumPy, which should be equivalent to a weighted moving average (WMA). When my weights are all equal (as in a simple arithmetic average), it works fine:

data = numpy.arange(1, 11)
numdays = 5
w = [1.0/numdays]*numdays
numpy.convolve(data, w, 'valid')


It gives:

array([ 3., 4., 5., 6., 7., 8.])


However, when I try to use a weighted average

w = numpy.cumsum(numpy.ones(numdays, dtype=float), axis=0); w = w/numpy.sum(w)


instead of the (for the same data) 3.667, 4.667, 5.667, 6.667,... I expect, I get

array([ 2.33333333, 3.33333333, 4.33333333, 5.33333333, 6.33333333,
7.33333333])


If I remove the 'valid' flag, I don't even see the correct values. I would really like to use convolve for the WMA as well as MA as it makes the code cleaner (same code, different weights) and otherwise I think I'll have to loop through all the data and take slices.

What causes this behavior?

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