We consider in this talk an I(d) autoregressive (AR) process, d >= 0 is an unknown integer. While Sin and Yu (2015) show that Akaike’s information criterion (AIC) is asymptotically inefficient when the lag order is finite; this talk shows that when the lag order is infinite with (a) exponentially decaying AR coefficients, or (b) algebraically decaying AR coefficients, Bayesian information criterion (BIC) is asymptotically inefficient. These results motivate us to combine the strengths of AIC and BIC, yielding a so-called twostage information criterion (TSIC) for a general I(d) AR process. We show that TSIC is asymptotically efficient in the aforementioned three scenarios. The talk concludes with a simulation study