Simulating the Eigenvalue Distribution Gauss file(s) coint_simevals.g Matlab file(s) coint_simevals.m

(a) Consider the bivariate VECM based on Model 1 in Table 18.1 with rank r = 1 y1,t = y2,t + v1,t , y2,t = y2,t−1 + v2,t , where vt = [v1,t, v2,t] ′ ∼ iid N(0, V ) with V = I2. Simulate the model 10000 times with samples of size T = {100, 200, 400, 800} and discuss the asymptotic properties of the sampling distributions of the estimated eigenvalues obtained from L −1S10S −1 00 S01L −1′ , where Si,j are defined in (18.25) with R0,t = ∆yt and R1,t = yt−1 and LL′ = S1,1.

(b) Repeat part

(a) for the trivariate VECM y1,t = 0.5y2,t + 0.5y3,t + v1,t y2,t = y2,t−1 + v2,t y3,t = y3,t−1 + v3,t .

(c) Repeat part

(a) for the trivariate VECM y1,t = y3,t + v1,t y2,t = y3,t + v1,t y3,t = y3,t−1 + v3,t .