Uniform Limit Theory for Stationary Autoregression
Liudas Giraitis (l.giraitis@qmul.ac.uk) and
Peter Phillips
Journal of Time Series Analysis, 2006, vol. 27, issue 1, 51-60
Abstract:
Abstract. First order autoregression is shown to satisfy a limit theory which is uniform over stationary values of the autoregressive coefficient ρ = ρn ∈ [0, 1) provided (1 − ρn)n → ∞. This extends existing Gaussian limit theory by allowing for values of stationary ρ that include neighbourhoods of unity provided they are wider than O(n−1), even by a slowly varying factor. Rates of convergence depend on ρ and are at least but less than n. Only second moments are assumed, as in the case of stationary autoregression with fixed ρ.
Date: 2006
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https://doi.org/10.1111/j.1467-9892.2005.00452.x
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Working Paper: Uniform limit theory for stationary autoregression
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