GARCH Multi-Step Variance Forecast

Problem

Forecast GARCH(1,1) conditional variances h steps ahead. Starting from sigma2, the first forecast is omega + alpha * e2 + beta * sigma2; each later forecast replaces the squared shock with its expectation, giving s_next = omega + (alpha + beta) * s.

Return the list of h forecasts, or an empty list when h is not positive.

Hint

Beyond the first step the shock has mean zero, so only persistence alpha + beta matters.

Test cases

case 1

in: [0.1,0.2,0.7,1,0.8,3]

expected: [0.86,0.8739999999999999,0.8865999999999998]

case 2

in: [0.05,0.1,0.8,0.5,0.3,2]

expected: [0.33999999999999997,0.356]

case 3

in: [0.1,0.3,0.6,2,1,1]

expected: [1.2999999999999998]

case 4

in: [0.1,0.2,0.7,1,0.8,0]

expected: []

Starter codePython

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

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