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Asymptotics for LS, GLS, and Feasible GLS Statistics in an AR(1) Model with Conditional Heteroskedaticity

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Abstract

This paper considers 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 and the distribution of the time series of innovations. In particular, we consider the full range of cases in which the autoregressive parameter rho_n satisfies (i) n(1 - rho_n) approaches infinity and (ii) n(1 - rho_n) approaches h_1

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  • Donald W.K. Andrews & Patrik Guggenberger, 2008. "Asymptotics for LS, GLS, and Feasible GLS Statistics in an AR(1) Model with Conditional Heteroskedaticity," Cowles Foundation Discussion Papers 1665, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1665
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    Cited by:

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    2. 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.
    3. Lu, Cuicui & Wooldridge, Jeffrey M., 2017. "Quasi-generalized least squares regression estimation with spatial data," Economics Letters, Elsevier, vol. 156(C), pages 138-141.
    4. 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.

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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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