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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.

Suggested Citation

  • Liudas Giraitis & Peter C.B. Phillips, 2004. "Uniform Limit Theory for Stationary Autoregression," Cowles Foundation Discussion Papers 1475, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1475
    Note: CFP 1166
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    Keywords

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

    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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