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Uniform Limit Theory for Stationary Autoregression


  • Liudas Giraitis
  • Peter C. B. Phillips


First order autoregression is shown to satisfy a limit theory which is uniform over stationary values of the autoregressive coefficient rho = rho_n is an element of [0, 1) provided (1 - rho_n)n goes to 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-super- - 1), even by a slowly varying factor. Rates of convergence depend on rho and are at least but less than n. Only second moments are assumed, as in the case of stationary autoregression with fixed rho. Copyright 2006 Blackwell Publishing Ltd.

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

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    References listed on IDEAS

    1. Klaus Frick & Axel Munk & Hannes Sieling, 2014. "Multiscale change point inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 495-580, June.
    2. Wenzhi Zhao & Zheng Tian & Zhiming Xia, 2010. "Ratio test for variance change point in linear process with long memory," Statistical Papers, Springer, vol. 51(2), pages 397-407, June.
    3. Fryzlewicz, Piotr, 2014. "Wild binary segmentation for multiple change-point detection," LSE Research Online Documents on Economics 57146, London School of Economics and Political Science, LSE Library.
    4. Inclan, Carla, 1993. "Detection of Multiple Changes of Variance Using Posterior Odds," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 289-300, July.
    5. Alexander Aue & Lajos Horváth, 2013. "Structural breaks in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 1-16, January.
    6. David S. Matteson & Nicholas A. James, 2014. "A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 334-345, March.
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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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