Subsampling realised kernels

Abstract

In a recent paper we have introduced the class of realised kernel estimators of the increments of quadratic variation in the presence of noise. We showed that this estimator is consistent and derived its limit distribution under various assumptions on the kernel weights. In this paper we extend our analysis, looking at the class of subsampled realised kernels and we derive the limit theory for this class of estimators. We find that subsampling is highly advantageous for estimators based on discontinuous kernels, such as the truncated kernel. For kinked kernels, such as the Bartlett kernel, we show that subsampling is impotent, in the sense that subsampling has no effect on the asymptotic distribution. Perhaps surprisingly, for the efficient smooth kernels, such as the Parzen kernel, we show that subsampling is harmful as it increases the asymptotic variance. We also study the performance of subsampled realised kernels in simulations and in empirical work.

Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading

“…Numerous problems and solutions are discussed in Falkenberry (2001), Hansen & Lunde (2006), Brownless & Gallo (2006) and Barndorff-Nielsen, Hansen, Lunde & Shephard (2008b). In this paper we follow the step-by-step cleaning procedure used in Barndorff-Nielsen et al (2008b) who discuss in detail the various choices available and their impact on univariate realised kernels. For convenience we briefly review these steps.…”

Forecasting Realized Volatility Using Subsample Averaging

“…More recent works investigating this issue include [3][4][5][6][7][8]. When the observed price process is the true underlying price process plus microstructure noise, it is shown that RV will be overwhelmed by the noise and explodes when the sampling frequency approaches infinity.…”

“…Therefore, it may be optimal to sample less frequently than is the case in the absence of noise. References [6,8] establish through a subsampling scheme improved estimators for quadratic variation. The original subsampling idea can be traced back to [9], where for the first time an unbiased datadriven estimator of volatility and a subsample averaging volatility estimator are proposed.…”

“…The bias-adjusted estimator of [6] based on the subsample averaging method is able to eventually push the estimation bias to zero. Reference [8] shows that subsampling is highly advantageous for RV estimators based on discontinuous kernels. tility estimation, volatility forecasting using high-frequency information has been addressed as well.…”

“…As shown by [6,8,9], subsampling schemes improve estimators for quadratic variation. When it comes to forecasting RV, if the highest frequency returns are not necessarily the optimal frequency, the subsampling of the available highest frequency data will lead to several systematically sampled subsamples.…”