Theil U Statistic

Problem

Compute Theil's U statistic comparing a forecast against the naive no-change forecast: U = sqrt(mean((forecast - actual)^2)) / sqrt(mean over t >= 1 of (actual[t] - actual[t-1])^2). Use the 1/m denominator in the numerator and 1/(m-1) in the denominator.

Return 0.0 if there are fewer than two actual values or the denominator is 0. U < 1 means the forecast beats a random walk.

Hint

The denominator is the RMSE of the naive persistence forecast.

Test cases

case 1

in: [[10,12,14],[11,11,11]]

expected: 0.9574271077563381

case 2

in: [[1,2,3,4],[1,2,3,4]]

expected: 0

case 3

in: [[5,5,5],[6,4,5]]

expected: 0

case 4

in: [[2,4,6,8],[3,5,7,8]]

expected: 0.4330127018922193

Starter codePython

def theil_u(actual, forecast):
    # Your code here
    pass

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