Holt-Winters Multiplicative One Step

Problem

Perform one multiplicative Holt-Winters update and return [level, trend, seasonal]. Given the old states and observation x: new_level = alpha * (x / seasonal) + (1 - alpha) * (level + trend); new_trend = beta * (new_level - level) + (1 - beta) * trend; new_seasonal = gamma * (x / new_level) + (1 - gamma) * seasonal.

The seasonal factor must be nonzero.

Hint

Multiplicative seasonality divides the observation by the seasonal factor instead of subtracting it.

Test cases

case 1

in: [10,0.5,1.5,12,0.5,0.3,0.4]

expected: [9.25,0.125,1.4189189189189189]

case 2

in: [5,0.2,2,6,0.4,0.3,0.2]

expected: [4.32,-0.06399999999999992,1.8777777777777778]

case 3

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

expected: [1,0,1]

case 4

in: [10,1,0.5,9,0.2,0.1,0.9]

expected: [12.4,1.1400000000000001,0.703225806451613]

Starter codePython

def holt_winters_multiplicative_step(level, trend, seasonal, x, alpha, beta, gamma):
    # Your code here
    pass

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