New asymptotic approximations are established for the Wald and t statistics in the presence of unknown but strong autocorrelation. The asymptotic theory extends the usual fixed-smoothing asymptotics under weak dependence to allow for near-unit-root and weak-unit-root processes. As the locality parameter that characterizes the neighborhood of the autoregressive root increases from zero to infinity, the new fixed-smoothing asymptotic distribution changes smoothly from the unit-root fixed-smoothing asymptotics to the usual fixed-smoothing asymptotics under weak dependence. Simulations show that the new approximation is more accurate than the usual fixed-smoothing approximation.
The ideas in the paper were first presented in my discussion of Müller (2014) at the 2013 ASSA meeting in San Diego, CA. For helpful comments, the author thanks Yoosoon Chang, Joon Park, Peter Phillips, an anonymous referee, and the participants of the 14th Advances in Econometrics Conference at Southern Methodist University in 2013.
Sun, Y. (2014), "Fixed-smoothing Asymptotics and Asymptotic
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