Ornstein-Uhlenbeck Process Gauss file(s) sim_ouind.g Matlab file(s) sim_ouind.m This exercise reproduces the Monte Carlo results presented in Gouri´eroux, Monfort and Renault (1993, Table III, p.S103). The Ornstein-Uhlenbeck process is given by dyt = α(κ − yt)dt + σdB , dB ∼ N(0, dt), where B(t) is a Wiener process. Let the sample size be T = 250 and the true parameters values be θ = {α = 0.1, κ = 0.8, σ = 0.062}. An exact discretization is yt+∆t = α(1 − exp[−κ∆t]) + exp[−κ∆t]yt + σ  1 − exp[−2κ∆t] 2κ  ut , where ut ∼ N(0, ∆t). Choose as the auxiliary model yt = (1 − κ∆t)yt−1 + κα∆t + σvt , vt ∼ N(0, ∆t).

(a) Compute the indirect estimates of the parameters for K = {10/∆t, 20/∆t} simulation paths where ∆t = 0.1.

(b) Compare the properties of the resultant estimators.