ACF Vector

Problem

Return the sample autocorrelation vector [rho(0), rho(1), ..., rho(h)] using the biased 1/n estimator: gamma(k) = (1/n) * sum over t < n-k of (x[t] - mean) * (x[t+k] - mean), and rho(k) = gamma(k) / gamma(0).

Lags with k >= n or a zero-variance series produce 0.0; return an empty list for h < 0 or an empty series.

Hint

The first element is always 1.0 for a non-constant series.

Test cases

case 1

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

expected: [1,0.25,-0.3]

case 2

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

expected: [1]

case 3

in: [[5,5,5],1]

expected: [0,0]

case 4

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

expected: [1,0.25,-0.3,-0.45,0]

Starter codePython

def acf_vector(series, h):
    # Your code here
    pass

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