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Asymptotics for LS, GLS, and feasible GLS statistics in an AR(1) model with conditional heteroskedasticity

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  • Andrews, Donald W.K.
  • Guggenberger, Patrik

Abstract

We consider a first-order autoregressive model with conditionally heteroskedastic innovations. The asymptotic distributions of least squares (LS), infeasible generalized least squares (GLS), and feasible GLS estimators and t statistics are determined. The GLS procedures allow for misspecification of the form of the conditional heteroskedasticity and, hence, are referred to as quasi-GLS procedures. The asymptotic results are established for drifting sequences of the autoregressive parameter ρn and the distribution of the time series of innovations. In particular, we consider the full range of cases in which ρn satisfies n(1−ρn)→∞ and n(1−ρn)→h1∈[0,∞) as n→∞, where n is the sample size. Results of this type are needed to establish the uniform asymptotic properties of the LS and quasi-GLS statistics.

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  • Andrews, Donald W.K. & Guggenberger, Patrik, 2012. "Asymptotics for LS, GLS, and feasible GLS statistics in an AR(1) model with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 169(2), pages 196-210.
    • Handle: RePEc:eee:econom:v:169:y:2012:i:2:p:196-210
    DOI: 10.1016/j.jeconom.2012.01.017
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    Cited by:

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    2. Westerlund, Joakim, 2014. "On the choice of test for a unit root when the errors are conditionally heteroskedastic," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 40-53.
    3. Ke-Li Xu, 2022. "On Local Projection Based Inference," CAEPR Working Papers 2022-002 Classification-, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    4. Ke-Li Xu, 2023. "Local Projection Based Inference under General Conditions," CAEPR Working Papers 2023-001 Classification-C, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    5. Chen, Ye & Phillips, Peter C.B. & Yu, Jun, 2017. "Inference in continuous systems with mildly explosive regressors," Journal of Econometrics, Elsevier, vol. 201(2), pages 400-416.
    6. Lu, Cuicui & Wooldridge, Jeffrey M., 2017. "Quasi-generalized least squares regression estimation with spatial data," Economics Letters, Elsevier, vol. 156(C), pages 138-141.

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    More about this item

    Keywords

    Asymptotic distribution; Autoregression; Conditional heteroskedasticity; Generalized least squares; Least squares;
    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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