MA(1) Autocovariances

Problem

Compute the lag-zero and lag-one autocovariances of an MA(1) process with coefficient theta and innovation variance sigma2. They are gamma0 = (1 + theta^2) * sigma2 and gamma1 = theta * sigma2.

Return a dict with keys gamma0 and gamma1.

Hint

All autocovariances beyond lag one are exactly zero for an MA(1).

Test cases

case 1

in: [0.5,1]

expected: {"gamma0":1.25,"gamma1":0.5}

case 2

in: [0,2]

expected: {"gamma0":2,"gamma1":0}

case 3

in: [1,4]

expected: {"gamma0":8,"gamma1":4}

case 4

in: [-0.5,2]

expected: {"gamma0":2.5,"gamma1":-1}

Starter codePython

def ma1_autocovariances(theta, sigma2):
    # Your code here
    pass

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