Long Run Variance Estimation Using Steep Origin Kernels without Truncation
AbstractA new class of kernel estimates is proposed for long run variance (LRV) and heteroskedastic autocorrelation consistent (HAC) estimation. The kernels are called steep origin kernels and are related to a class of sharp origin kernels explored by the authors (2003) in other work. They are constructed by exponentiating a mother kernel (a conventional lag kernel that is smooth at the origin) and they can be used without truncation or bandwidth parameters. When the exponent is passed to infinity with the sample size, these kernels produce consistent LRV/HAC estimates. The new estimates are shown to have limit normal distributions, and formulae for the asymptotic bias and variance are derived. With steep origin kernel estimation, bandwidth selection is replaced by exponent selection and data-based selection is possible. Rules for exponent selection based on minimum mean squared error (MSE) criteria are developed. Optimal rates for steep origin kernels that are based on exponentiating quadratic kernels are shown to be faster than those based on exponentiating the Bartlett kernel, which produces the sharp origin kernel. It is further shown that, unlike conventional kernel estimation where an optimal choice of kernel is possible in terms of MSE criteria (Priestley, 1962; Andrews, 1991), steep origin kernels are asymptotically MSE equivalent, so that choice of mother kernel does not matter asymptotically. The approach is extended to spectral estimation at frequencies omega
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Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1437.
Length: 47 pages
Date of creation: Sep 2003
Date of revision:
Publication status: Published in Journal of Statistical Planning and Inference (2007), 137: 985-1023
Note: CFP 1178
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Other versions of this item:
- Peter C.B. Phillips & Sainan Jin & Yixiao Sun, 2004. "Long Run Variance Estimation Using Steep Origin Kernels Without Truncation," Yale School of Management Working Papers ysm427, Yale School of Management.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2003-10-12 (All new papers)
- NEP-ECM-2003-10-12 (Econometrics)
- NEP-ETS-2003-10-12 (Econometric Time Series)
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- Ole E Barndorff-Nielsen & Peter Hansen & Asger Lunde & Neil Shephard, 2006.
"Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise,"
OFRC Working Papers Series
2006fe05, Oxford Financial Research Centre.
- Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
- Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Papers 2006-W03, Economics Group, Nuffield College, University of Oxford.
- Neil Shephard & Ole E. Barndorff-Nielsen, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Series Working Papers 2006-W03, University of Oxford, Department of Economics.
- Peter C.B. Phillips & Yixiao Sun & Sainan Jin, 2005. "Improved HAR Inference," Cowles Foundation Discussion Papers 1513, Cowles Foundation for Research in Economics, Yale University.
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