AR(2) Simulated Variance

Problem

Simulate an AR(2) process x[t] = phi1 * x[t-1] + phi2 * x[t-2] + e[t] with standard normal innovations and return the population variance of the generated values. Call random.seed(seed), discard the first 100 observations as burn-in, then collect n values.

Return 0.0 if n is not positive. The parameter pair is assumed to satisfy the stationarity conditions.

Hint

Keep the last two simulated values in a small list and append each new draw.

Test cases

case 1

in: [0.5,0.2,200,42]

expected: 1.7542622157049643

case 2

in: [0.3,-0.4,200,7]

expected: 1.2567030545273807

case 3

in: [0.6,0.3,200,1]

expected: 3.835498405994975

case 4

in: [0,0,200,5]

expected: 1.009451643912433

Starter codePython

import random
def ar2_simulated_variance(phi1, phi2, n, seed):
    # Your code here
    pass

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