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Adaptive Inference In Heteroskedastic Fractional Time Series Models


  • Giuseppe Cavaliere

    (University of Bologna)

  • Morten Ø. Nielsen

    () (Queen's University and CREATES)

  • A.M. Robert Taylor

    (University of Essex)


We consider estimation and inference in fractionally integrated time series models driven by shocks which can display conditional and unconditional heteroskedasticity of unknown form. Although the standard conditional sum-of-squares (CSS) estimator remains consistent and asymptotically normal in such cases, unconditional heteroskedasticity inflates its variance matrix by a scalar quantity, lambda>1, thereby inducing a loss in efficiency relative to the unconditionally homoskedastic case, lambda=1. We propose an adaptive version of the CSS estimator, based on non-parametric kernel-based estimation of the unconditional variance process. This eliminates the factor lambda from the variance matrix, thereby delivering the same asymptotic efficiency as that attained by the standard CSS estimator in the unconditionally homoskedastic case and, hence, asymptotic efficiency under Gaussianity. The asymptotic variance matrices of both the standard and adaptive CSS estimators depend on any conditional heteroskedasticity and/or weak parametric autocorrelation present in the shocks. Consequently, asymptotically pivotal inference can be achieved through the development of confidence regions or hypothesis tests using either heteroskedasticity robust standard errors and/or a wild bootstrap. Monte Carlo simulations and empirical applications are included to illustrate the practical usefulness of the methods proposed.

Suggested Citation

  • Giuseppe Cavaliere & Morten Ø. Nielsen & A.M. Robert Taylor, 2019. "Adaptive Inference In Heteroskedastic Fractional Time Series Models," Working Paper 1390, Economics Department, Queen's University.
  • Handle: RePEc:qed:wpaper:1390

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    More about this item


    adaptive estimation; conditional sum-of-squares; fractional integration; heteroskedasticity; quasi-maximum likelihood estimation; wild bootstrap;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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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