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Lower Risk Bounds and Properties of Confidence Sets For Ill-Posed Estimation Problems with Applications to Spectral Density and Persistence Estimation, Unit Roots,and Estimation of Long Memory Parameters



Important estimation problems in econometrics like estimation the value of a spectral density at frequency zero, which appears in the econometrics literature in the guises of heteroskedasticity and autocorrelation consistent variance estimation and long run variance estimation, are shown to be "ill-posed" estimation problems. A prototypical result obtained in the paper is that the minimax risk for estimation the value of the spectral density at frequency zero is infinite regardless of sample size, and that confidence sets are close to being univormative. In this result the maximum risk is over commonly used specifications for the set of feasible data generating processes. The consequences for inference on unit roots and cointegrating are discussed. Similar results for persistence estimation and estimation of the long memory parameter are given. All these results are obtained as special cases of a more general theory developed for abstract estimation problems, which readily also allows for the treatment of other ill-posed estimation problems such as, e. g. nonparametric regression of density estimation.

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  • Benedikt M. Pötscher, 1999. "Lower Risk Bounds and Properties of Confidence Sets For Ill-Posed Estimation Problems with Applications to Spectral Density and Persistence Estimation, Unit Roots,and Estimation of Long Memory Paramet," Vienna Economics Papers 0202, University of Vienna, Department of Economics.
  • Handle: RePEc:vie:viennp:0202

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    Cited by:

    1. DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing," Cahiers de recherche 16-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. Zhijie Xiao & Luiz Renato Lima, 2007. "Testing Covariance Stationarity," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 643-667.
    3. Dufour, Jean-Marie & Jouini, Tarek, 2006. "Finite-sample simulation-based inference in VAR models with application to Granger causality testing," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 229-254.
    4. Davidson James & Rambaccussing Dooruj, 2015. "A Test of the Long Memory Hypothesis Based on Self-Similarity," Journal of Time Series Econometrics, De Gruyter, vol. 7(2), pages 115-141, July.
    5. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2007. "A simple, robust and powerful test of the trend hypothesis," Journal of Econometrics, Elsevier, vol. 141(2), pages 1302-1330, December.
    6. Preinerstorfer, David & Pötscher, Benedikt M., 2016. "On Size And Power Of Heteroskedasticity And Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 32(02), pages 261-358, April.
    7. Muller, Ulrich K., 2007. "A theory of robust long-run variance estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1331-1352, December.
    8. Xiao, Zhijie, 2012. "Robust inference in nonstationary time series models," Journal of Econometrics, Elsevier, vol. 169(2), pages 211-223.
    9. Tsay, Wen-Jen, 2004. "Testing for contemporaneous correlation of disturbances in seemingly unrelated regressions with serial dependence," Economics Letters, Elsevier, vol. 83(1), pages 69-76, April.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: 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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