MA(1) Process Generation

Problem

Generate a seeded MA(1) process. Call random.seed(seed), draw n standard normal innovations e[t] with random.gauss(0.0, 1.0), and return y[t] = e[t] + theta * e[t-1] for t >= 1 with y[0] = e[0].

Return an empty list when n is not positive.

Hint

Seeding inside the function keeps the output reproducible.

Test cases

case 1

in: [5,0.5,42]

expected: [-0.14409032957792836,-0.24494876512048347,-0.1977676617334221,0.6463257943150319,0.22340357876654446]

case 2

in: [4,-0.3,7]

expected: [-0.2558802884476004,0.5881955990507941,-0.3795256185380589,-0.24723957289625403]

case 3

in: [3,0,1]

expected: [1.2881847531554629,1.4494456086997711,0.06633580893826191]

case 4

in: [0,0.5,3]

expected: []

Starter codePython

import random
def ma1_generate(n, theta, seed):
    # Your code here
    pass

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