GARCH(1,1) Variance Update

Problem

Update the conditional variance of a GARCH(1,1) model: sigma2_new = omega + alpha * e^2 + beta * sigma2, where e is the latest innovation and sigma2 the previous conditional variance.

Return the updated variance.

Hint

Persistence is alpha + beta; large shocks raise next period's variance.

Test cases

case 1

in: [0.1,0.1,0.8,4,1]

expected: 1.3

case 2

in: [0.2,0.3,0.5,1,2]

expected: 1.5

case 3

in: [0,0,0,5,5]

expected: 0

case 4

in: [0.1,0.2,0.7,0,0]

expected: 0.1

Starter codePython

def garch11_update(omega, alpha, beta, e2, sigma2):
    # Your code here
    pass

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