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Uniform Limit Theory for Stationary Autoregression

Author

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  • Liudas Giraitis
  • Peter C. B. Phillips

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.

Suggested Citation

  • Liudas Giraitis & Peter C. B. Phillips, 2006. "Uniform Limit Theory for Stationary Autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 51-60, January.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:1:p:51-60
    DOI: 10.1111/j.1467-9892.2005.00452.x
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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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