AR(1) Process Generation

Problem

Generate a seeded AR(1) process. Call random.seed(seed), draw n standard normal innovations, and initialize x[0] = c / (1 - phi) + e[0] when abs(phi) < 1 (otherwise x[0] = e[0]); then iterate x[t] = c + phi * x[t-1] + e[t].

Return the generated series; n <= 0 gives an empty list.

Hint

Start from the stationary mean c / (1 - phi) so burn-in is unnecessary.

Test cases

case 1

in: [5,0.5,0.5,42]

expected: [0.8559096704220717,0.7550512348795165,0.7662097558720958,1.5850886030349112,1.1649560177345686]

case 2

in: [4,1,0,7]

expected: [0.7441197115523996,1.511431512516514,0.7739038352168953,0.6849315776688145]

case 3

in: [3,0.2,-0.5,1]

expected: [1.4215180864887962,0.9386865654553731,-0.20300747378942463]

case 4

in: [0,0.5,0.5,3]

expected: []

Starter codePython

import random
def ar1_generate(n, c, phi, seed):
    # Your code here
    pass

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