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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 in [0,infinity) as n approaches infinity, 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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  • 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 1665R, Cowles Foundation for Research in Economics, Yale University, revised Mar 2010.
  • Handle: RePEc:cwl:cwldpp:1665r
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    1. repec:eee:econom:v:201:y:2017:i:2:p:400-416 is not listed on IDEAS
    2. repec:eee:ecolet:v:156:y:2017:i:c:p:138-141 is not listed on IDEAS

    More about this item

    Keywords

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

    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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