First order autoregression is shown to satisfy a limit theory which is uniform over stationary values of the autoregressive coefficient rho = rho_{n} in [0,1) provided (1 - rho_{n})n approaches infinity. This extends existing Gaussian limit theory by allowing for values of stationary rho that include neighbourhoods of unity provided they are wider than O(n^{1}), even by a slowly varying factor. Rates of convergence depend on rho and are at least squareroot of squareroot of n but less than n. Only second moments are assumed, as in the case of stationary autoregression with fixed rho.
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Length: 9 pages Date of creation: Jul 2004 Date of revision: Publication status: Published in Journal of Time Series Analysis (2006), 27(1): 51-60 Handle: RePEc:cwl:cwldpp:1475
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