D.1 Parameters in a Simulation

Which quantities are known vs unknown if you want to simulate a specific ARMA(p,q) model?

known (set up before simulation):

• Orders p and q
• Starting parameters for ARMA(p, q)
• Bounds for ARMA parameters
• Amount of periods T to be simulated
• Amount of random paths P per each time period (can be arbitrarily large because there are an infinite number of possibilities)
• Seed of the random number generator

unknown (would be simulated):

• Matrix of White Noise shocks with dimension T x P.

D.2 Random Number Generator

What characterizes a good random number generator?

Good random number generator:

• has a long period (produces many distinct values before repeating)
• allows to reproduce any random sequence
• is fast
• is portable across computing platforms
• produces the output, that appears statistically random

E. Exercises - Challenging