Simulate a random walk (left{z_{t} ight}) of length 500 . Now generate two series, (left{x_{t} ight}) and (left{y_{t} ight}), each of which follows the random

Simulate a random walk \(\left\{z_{t}\right\}\) of length 500 . Now generate two series, \(\left\{x_{t}\right\}\) and \(\left\{y_{t}\right\}\), each of which follows the random walk with an additive white noise, one with variance \(\sigma_{1}^{2}=1\) and the other with variance \(\sigma_{2}^{2}=9\).

Perform a Phillips-Ouliaris cointegration test on the two simulated series.