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

Peter Phillips, Yixiao Sun and Sainan Jin

University of California at San Diego, Economics Working Paper Series from Department of Economics, UC San Diego

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.

Keywords: Exponentiated Kernel; Lag Kernel; Long Run Variance; Optimal Exponent; Spectral Window; Spectrum (search for similar items in EconPapers)
Date: 2004-11-01
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Journal Article: SPECTRAL DENSITY ESTIMATION AND ROBUST HYPOTHESIS TESTING USING STEEP ORIGIN KERNELS WITHOUT TRUNCATION (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:cdl:ucsdec:qt6mf9q2rt

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