Long-Run Variance Multiplier

Problem

Compute the long-run variance multiplier of a stationary series from its autocorrelations. For a list of autocorrelations r1, ..., rm, the multiplier is 1 + 2 * (r1 + ... + rm), which scales the variance when summing a long block of observations.

An empty list of autocorrelations gives a multiplier of 1.0.

Hint

Each autocorrelation appears twice in the double sum, once for +k and once for -k.

Test cases

case 1

in: [[0.5]]

expected: 2

case 2

in: [[0.5,0.25]]

expected: 2.5

case 3

in: [[]]

expected: 1

case 4

in: [[-0.25,0]]

expected: 0.5

Starter codePython

def long_run_variance_multiplier(rhos):
    # Your code here
    pass

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