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Mean and autocovariance function estimation near the boundary of stationarity

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  • Giraitis, Liudas
  • Phillips, Peter C.B.

Abstract

We analyze the applicability of standard normal asymptotic theory for linear process models near the boundary of stationarity. Limit results are given for estimation of the mean, autocovariance and autocorrelation functions within the broad region of stationarity that includes near boundary cases which vary with the sample size. The rate of consistency and the validity of the normal asymptotic approximation for the corresponding estimators is determined both by the sample size n and a parameter measuring the proximity of the model to the unit root boundary.

Suggested Citation

  • Giraitis, Liudas & Phillips, Peter C.B., 2012. "Mean and autocovariance function estimation near the boundary of stationarity," Journal of Econometrics, Elsevier, vol. 169(2), pages 166-178.
    • Handle: RePEc:eee:econom:v:169:y:2012:i:2:p:166-178
    DOI: 10.1016/j.jeconom.2012.01.020
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    References listed on IDEAS

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    1. 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.
    2. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    3. Phillips,Garry D. A. & Tzavalis,Elias (ed.), 2007. "The Refinement of Econometric Estimation and Test Procedures," Cambridge Books, Cambridge University Press, number 9780521870535, November.
    4. R J Bhansali & L Giraitis & P Kokoszka, "undated". "Decomposition and asymptotic properties of quadratic forms in linear variables," Discussion Papers 05/18, Department of Economics, University of York.
    5. Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, vol. 73(1), pages 261-284, July.
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    Cited by:

    1. Yabe, Ryota, 2017. "Asymptotic distribution of the conditional-sum-of-squares estimator under moderate deviation from a unit root in MA(1)," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 220-226.
    2. Karavias, Yiannis & Symeonides, Spyridon D. & Tzavalis, Elias, 2018. "Higher order expansions for error variance matrix estimates in the Gaussian AR(1) linear regression model," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 54-59.
    3. Stauskas, Ovidijus, 2019. "On the Limit Theory of Mixed to Unity VARs: Panel Setting With Weakly Dependent Errors," Working Papers 2019:2, Lund University, Department of Economics.
    4. Ovidijus Stauskas, 2020. "On the limit theory of mixed to unity VARs: Panel setting with weakly dependent errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 892-898, November.
    5. Bailey, N. & Giraitis, L., 2013. "Weak convergence in the near unit root setting," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1411-1415.

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    More about this item

    Keywords

    Asymptotic normality; Integrated periodogram; Linear process; Local to unity; Localizing coefficient;
    All these keywords.

    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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