Thinned Autocorrelation

Problem

If a Markov chain has lag-1 autocorrelation rho, keeping every k-th sample (thinning) reduces the lag-1 autocorrelation to:

rho_thinned = rho^k.

Return 0.0 for k < 0.

Hint

Autocorrelation decays geometrically under an AR(1)-like chain.

case 1

in: [0.9,10]

expected: 0.3486784401000001

case 2

in: [0.5,3]

expected: 0.125

case 3

in: [0.9,0]

expected: 1

case 4

in: [0.5,-1]

expected: 0

Starter codePython

def thinned_autocorrelation(rho, k):
    # Your code here
    pass

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