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Uniform limit theory for stationary autoregression

Author

Listed:
  • L Giraitis
  • P C B Phillips

Abstract

First order autoregression is shown to satisfy a limit theory which is uniform over stationary values of the autoregressive coefficient ?=?_{n}?[0,1) provided (1-?_{n})n??. This extends existing Gaussian limit theory by allowing for values of stationary ? that include neighbourhoods of unity provided they are wider than O(1/n), even by a slowly varying factor. Rates of convergence depend on ? and are at least ?n but less than n. Only second moments are assumed, as in the case of stationary autoregression with fixed ?.

Suggested Citation

  • L Giraitis & P C B Phillips, "undated". "Uniform limit theory for stationary autoregression," Discussion Papers 05/23, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:05/23
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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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