Autocovariance Lag k

Problem

Compute the sample autocovariance at lag k using the biased 1/n denominator: gamma(k) = (1/n) * sum over t = 0, ..., n-k-1 of (x[t] - mean) * (x[t+k] - mean).

Return 0.0 if k is negative or k is at least n.

Hint

Always divide by the full length n, not by n - k; that is the biased estimator.

Test cases

case 1

in: [[1,2,3,4],0]

expected: 1.25

case 2

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

expected: 0.3125

case 3

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

expected: -0.375

case 4

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

expected: 0

Starter codePython

def autocovariance(series, k):
    # Your code here
    pass

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