KPSS Level Statistic Lite

Problem

Compute the KPSS level stationarity statistic. Let S_t be the partial sums of the demeaned series; the statistic is sum(S_t^2) / (n^2 * sample_variance), using the population variance as the long-run variance estimate.

Return 0.0 for fewer than two observations or a constant series.

Hint

Trending series have partial sums that drift far from zero, inflating the statistic.

Test cases

case 1

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

expected: 0.4166666666666667

case 2

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

expected: 0

case 3

in: [[1]]

expected: 0

case 4

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

expected: 0.08333333333333333

case 5

in: [[2,4,6,8,10]]

expected: 0.52

Starter codePython

def kpss_level_statistic(series):
    # Your code here
    pass

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