Detrended Fluctuation

Problem

Compute a single-scale detrended fluctuation. Integrate the mean-adjusted series into a profile, detrend the profile with an OLS line against time, and return the root mean squared residual.

Return 0.0 for fewer than two points.

Hint

Detrending the integrated profile removes slow drift before measuring fluctuation.

Test cases

case 1

in: [[1,2,3,4,5]]

expected: 0.8366600265340756

case 2

in: [[5,5,5]]

expected: 0

case 3

in: [[1,-1,1,-1]]

expected: 0.4472135954999579

case 4

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

expected: 0.2390457218668787

Starter codePython

def detrended_fluctuation(series):
    # Your code here
    pass

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