Increased Moving Averages

Question

I want to calculate the increased moving averages.

My main aim is to get increased MAs, such that first MA is average of first value, next MA is Average of first 2 values, next MA is Average of first 4 values, next MA is Average of first 6 values and so on.

How can I do this using numpy library in Python?

I am doing my analysis on time series data using Python. I am also interested in moving averages, to calculate moving averages for my target variable, I used the following function to calculate MA over my target variable.

def movingaverage(values, avg_number):
    weights = np.repeat(1.0, avg_number)/avg_number
    smas = np.convolve(values, weights, 'valid')
    return smas

In this function, I supply my pandas Series and the average number to calc. corresponding averages.

Now, I want to calculate increased moving averages. like in the above the averages are being calculated over fixed number, say 90.

But, in case of reduced/increased moving averages, this number will reduce/increase at each next value.

My main aim is to get increased MAs, such that first MA is average of first value, next MA is Average of first 2 values, next MA is Average of first 4 values, next MA is Average of first 6 values and so on.

How can I do this using numpy library in Python?

If input is [1,5,3,6,8,4,6,8,4,2,3,5,8,6,4] and output will be increased moving averages like [1,3,3,3.75....]

Answer 1

You can use cumsum and np.arange i.e

x = np.array([1,5,3,6,8,4,6,8,4,2,3,5,8,6,4])
y = x.cumsum()/np.arange(1,len(x)+1)

Output :

array([ 1.        ,  3.        ,  3.        ,  3.75      ,  4.6       ,
     4.5       ,  4.71428571,  5.125     ,  5.        ,  4.7       ,
     4.54545455,  4.58333333,  4.84615385,  4.92857143,  4.86666667])