SES Closed-Form Forecast from Initial Level

Problem

Compute the simple exponential smoothing level after passing through the whole series, starting from a supplied initial level l0. Instead of iterating, use the closed form: (1 - alpha)^n * l0 plus alpha times the geometrically weighted sum of the observations, with the most recent observation weighted most.

Return l0 itself for an empty series.

Hint

The initial level inherits the weight (1 - alpha)^n after n observations.

Test cases

case 1

in: [[1,2,3],0.5,0]

expected: 2.125

case 2

in: [[10],0.4,5]

expected: 7

case 3

in: [[],0.5,3]

expected: 3

case 4

in: [[1,2],1,0]

expected: 2

Starter codePython

def ses_closed_form(series, alpha, l0):
    # Your code here
    pass

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