Consider an autoregressive model (with iid homoskedastic errors, stationary) where the lag length is one. The researcher knows that the true lag length is no bigger than 2. Use the BIC to estimate the lag length, p, and denotes the estimated lag length by the BIC \hat{p}_{BIC}. Prove that: Pr(\hat{p}_{BIC} = 0) \to 0, Pr(\hat{p}_{BIC} = 2) \to 0