Statistics Seminar: CY SIN -- Asymptotic inefficiency of BIC and asymptotic efficiency of TSIC: the case of an I(d) process

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