ARCH(q) Variance

Problem

Compute the conditional variance of an ARCH(q) model: sigma2 = omega + sum over i of alpha_i * e2_lag_i, pairing alphas and lagged squared shocks in order.

Extra coefficients or shocks beyond the shorter list are ignored.

Hint

With no lag terms the conditional variance collapses to the long-run constant omega.

Test cases

case 1

in: [0.05,[0.3,0.2],[1,0.5]]

expected: 0.44999999999999996

case 2

in: [0.1,[],[]]

expected: 0.1

case 3

in: [0.02,[0.5],[0.04]]

expected: 0.04

case 4

in: [0,[0.1,0.1,0.1],[1,2,3]]

expected: 0.6000000000000001

Starter codePython

def arch_q_variance(omega, alphas, lagged_sq):
    # Your code here
    pass

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