Linearly Weighted Moving Average

Problem

Compute a linearly weighted moving average for every full window of size k, giving the oldest value in a window weight 1 and the newest weight k. Each window average is the dot product of the window with the weights 1, 2, ..., k divided by k * (k + 1) / 2.

Return an empty list when k is not positive or when k exceeds the series length.

Hint

Newer observations carry more weight, so the average lags the raw series less than an SMA.

Test cases

case 1

in: [[1,2,3],2]

expected: [1.6666666666666667,2.6666666666666665]

case 2

in: [[1,2,3],3]

expected: [2.3333333333333335]

case 3

in: [[5],1]

expected: [5]

case 4

in: [[1,2],3]

expected: []

Starter codePython

def linearly_weighted_average(series, k):
    # Your code here
    pass

4 test cases · run your code against them in the editor