Unit Root Test without Lags or Long-Run Variance Gauss file(s) unit_breitung_size.g, unit_breitung_power.g Matlab file(s) unit_breitung_size.m, unit_breitung_power.m Consider the AR(1) model yt = yt1 + vt

Unit Root Test without Lags or Long-Run Variance Gauss file(s) unit_breitung_size.g, unit_breitung_power.g Matlab file(s) unit_breitung_size.m, unit_breitung_power.m Consider the AR(1) model yt = φyt−1 + vt where vt is a disturbance satisfying the same conditions as set out in Exercise 6. Consider the unit root test statistic ρ = T −4 PT t=1 S 2 t T −2 PT t=1 y 2 t , where St = Pt j=1 yj , as proposed by Breitung (2002).

(a) Show that the asymptotic distribution of this statistic under H0 : φ = 1 is ρ d → R 1 0 BS(r) 2dr R 1 0 B(r) 2dr , where BS(r) = R r 0 B(s)ds, regardless of the autocorrelation properties of vt (no autoregression or long-run variance is required to make this test operational).

(b) Carry out a Monte Carlo experiment to investigate the finite sample size properties of this test. Use the design from part d of the previous exercise.

(c) Use a simulation to compare the asymptotic local power of the test to that of the DFt test.