Suppose a time series X0, X1, X2,... evolves in the following way.

The process starts at 0, so X0 = 0. For any i ≥ 1, conditional on X0,..., Xi−1, Xi =

ρXi−1 + i , where the i are i.i.d. standard normal. You observe X0, X1, X2,..., Xn.

For testing the null hypothesis ρ = 0 versus ρ > 0, determine both Wald and Rao score tests as well as appropriate critical values. (Compare with Problems 3.35 and 14.49).