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<p>Realized kernels (RK) of Barndorff-Nielsen et&#xa0;al. (Econometrica 76:1481–1536, 2008) are consistent estimators of daily integrated volatility (IV) under dependent exogenous and endogenous market microstructure noise (MMN), if the bandwidth is properly selected. We propose to calculate RK with an iterative plug-in (IPI) bandwidth selector by adapting the idea of Barndorff-Nielsen et&#xa0;al. (Econometr J 12:C1–C32, 2009). Under independent MMN, the IPI bandwidth converges (relatively) at the rate <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n^{-1/5}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>n</mi> <mrow> <mo>-</mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>5</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>. The selected bandwidth under dependent MMN also converges up to a bias factor. In both cases the resulting RK achieves its best rate of convergence of the order <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(O_p(n^{-1/5})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>O</mi> <mi>p</mi> </msub> <mrow> <mo stretchy="false">(</mo> <msup> <mi>n</mi> <mrow> <mo>-</mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>5</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> in the current context. The proposal is applied to a huge number of data examples. Its nice practical performance is further confirmed in a simulation with the approach of Barndorff-Nielsen et&#xa0;al. (Econometr J 12:C1–C32, 2009) and its resulting RK as comparisons. It shows that the IPI-algorithm and the resulting RK perform better than the comparisons, respectively.</p>

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An iterative plug-in algorithm for realized kernels

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  • 发表日期：

    2026年5月14日

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  • Yuanhua Feng,
  • Chen Zhou

摘要

Realized kernels (RK) of Barndorff-Nielsen et al. (Econometrica 76:1481–1536, 2008) are consistent estimators of daily integrated volatility (IV) under dependent exogenous and endogenous market microstructure noise (MMN), if the bandwidth is properly selected. We propose to calculate RK with an iterative plug-in (IPI) bandwidth selector by adapting the idea of Barndorff-Nielsen et al. (Econometr J 12:C1–C32, 2009). Under independent MMN, the IPI bandwidth converges (relatively) at the rate \(n^{-1/5}\) n - 1 / 5 . The selected bandwidth under dependent MMN also converges up to a bias factor. In both cases the resulting RK achieves its best rate of convergence of the order \(O_p(n^{-1/5})\) O p ( n - 1 / 5 ) in the current context. The proposal is applied to a huge number of data examples. Its nice practical performance is further confirmed in a simulation with the approach of Barndorff-Nielsen et al. (Econometr J 12:C1–C32, 2009) and its resulting RK as comparisons. It shows that the IPI-algorithm and the resulting RK perform better than the comparisons, respectively.