Ljung-Box Statistic Lite

Problem

Compute the Ljung-Box portmanteau statistic from a list of sample autocorrelations: Q = n * (n + 2) * sum over k = 1..h of rho_k^2 / (n - k), where rho_k is acf_values[k-1].

Return 0.0 if h is not positive or n <= h. Larger Q indicates stronger serial correlation.

Hint

Each lag is weighted by 1 / (n - k), which grows with k.

Test cases

case 1

in: [[0.2,-0.1,0.05],100,3]

expected: 5.424915045680878

case 2

in: [[0.5,-0.3,0.2,0.1],50,4]

expected: 20.918289471200133

case 3

in: [[0.1],20,1]

expected: 0.2315789473684211

case 4

in: [[0.9],10,1]

expected: 10.8

Starter codePython

def ljung_box(acf_values, n, h):
    # Your code here
    pass

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