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Spectral Density Estimation and Robust Hypothesis Testing Using Steep Origin Kernels Without Truncation

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Author Info
Peter Phillips (Yale University, University of Auckland, University of York)
Yixiao Sun (University of California, San Diego)
Sainan Jin (Peking University)

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Abstract

In this paper, we construct a new class of kernel by exponentiating conventional kernels and use them in the long run variance estimation with and without smoothing. Depending on whether the exponent is allowed to grow with the sample size, we establish different asymptotic approximations to the sampling distribution of the proposed estimator. When the exponent is passed to infinity with the sample size, the new estimator is consistent and shown to be asymptotically normal. When the exponent is fixed, the new estimator is inconsistent and has a nonstandard limiting distribution. It is shown via Monte Carlo experiments that, when the chosen exponent is small in practical applications, the nonstandard limit theory provides better approximations to the finite sampling distributions of the spectral density estimator and the associated test statistic in regression settings.

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Publisher Info
Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number 2004-15.

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Date of creation: 01 Nov 2004
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Handle: RePEc:cdl:ucsdec:2004-15

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Related research
Keywords: Exponentiated Kernel Lag Kernel Long Run Variance Optimal Exponent Spectral Window Spectrum

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  1. M. Hashem Pesaran & Allan Timmermann, 2006. "Testing Dependence among Serially Correlated Multi-category Variables," CESifo Working Paper Series CESifo Working Paper No. , CESifo GmbH. [Downloadable!]
    Other versions:
  2. Douglas Steigerwald & Jack Erb, 2007. "Accurately Sized Test Statistics with Misspecified Conditional Homoskedasticity," University of California at Santa Barbara, Economics Working Paper Series 09-07, Department of Economics, UC Santa Barbara. [Downloadable!]
Statistics
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