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Uniform Limit Theory for Stationary Autoregression

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Abstract

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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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1475.

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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

Note: CFP 1166
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Autoregression; Gaussian limit theory; local to unity; uniform limit;

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