Uniform limit theory for stationary autoregression

Liudas Giraitis () and Peter Phillips

Discussion Papers from Department of Economics, University of York

Abstract: First order autoregression is shown to satisfy a limit theory which is uniform over stationary values of the autoregressive coefficient ?=?_{n}?[0,1) provided (1-?_{n})n??. This extends existing Gaussian limit theory by allowing for values of stationary ? that include neighbourhoods of unity provided they are wider than O(1/n), even by a slowly varying factor. Rates of convergence depend on ? and are at least ?n but less than n. Only second moments are assumed, as in the case of stationary autoregression with fixed ?.

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Related works:
Journal Article: Uniform Limit Theory for Stationary Autoregression (2006)
Working Paper: Uniform Limit Theory for Stationary Autoregression (2004)
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