Trend Misspecification Gauss file(s) nts_trend.g Matlab file(s) nts_trend.m (a) Simulate the random walk with drift yt = + yt1 + vt , vt

Trend Misspecification Gauss file(s) nts_trend.g Matlab file(s) nts_trend.m

(a) Simulate the random walk with drift yt = δ + yt−1 + vt , vt ∼ N(0, σ2 ), where δ = 0.5, σ 2 = 1 and y0 = 0 for a sample size of T = 100. Using the simulated data, estimate the deterministic trend model yt = β0 + β1t + et , and comment on the parameter estimates βb 0 and βb 1.

(b) Repeat part

(a) with drift parameter δ = 1.0.

(c) Repeat parts

(a) and

(b) for T = 1000.

(d) Simulate the random walk with drift model in part

(a) 50000 times for a sample of size T = 5000. Compute the mean and the variance of the sampling distribution of βb 1 in the deterministic trend model of part

(a) and compare these statistics with the moments of the asymptotic distribution N(0, 6σ 2/5) derived in (16.41).