MediumStatisticsst-217

AR(1) Covariance

Problem

Return the n-by-n AR(1) covariance matrix with entries sigma_sq * rho^|i-j|. Return [] when n <= 0 or sigma_sq < 0.

Hint

Correlation decays geometrically with the time gap.

case 1

in: [1,0.5,3]

expected: [[1,0.5,0.25],[0.5,1,0.5],[0.25,0.5,1]]

case 2

in: [2,0,2]

expected: [[2,0],[0,2]]

case 3

in: [1,-0.5,2]

expected: [[1,-0.5],[-0.5,1]]

case 4

in: [1,0.5,1]

expected: [[1]]

case 5

in: [1,0.5,0]

expected: []

Starter codePython

def ar1_covariance(sigma_sq, rho, n):
    # Your code here
    pass

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