Realized
Kernels and Market Microstructure Noise
Research
by BNHLS
Multivariate Realised
Kernels: Consistent Positive Semi-Definite Estimators of the Covariation of
Equity Prices with Noise and Non-Synchronous Trading
Abstract: We propose a
multivariate realised kernel to estimate the ex-post covariation of log-prices.
We show this new consistent estimator is guaranteed to be positive semi-definite
and is robust to measurement noise of certain types and can also handle
non-synchronous trading. It is the first estimator which has these three
properties which are all essential for empirical work in this area. We derive
the large sample asymptotics of this estimator and assess its accuracy using a
Monte Carlo study. We implement the estimator on some US equity data, comparing
our results to previous work which has used returns measured over 5 or 10
minutes intervals. We show the new estimator is substantially more precise.
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Paper
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Appendix with additional results and estimations
Realized Kernels in Practice: Trades and Quotes
Forthcoming in Econometrics
Journal
Abstract: Realised kernels
use high frequency data to estimate daily volatility of individual stock prices.
They can be applied to either trade or quote data. Here we provide the details
of how we suggest implementing them in practice. We compare the estimates based
on trade and quote data for the same stock and find a remarkable level of
agreement. We identify some features of the high frequency data which are
challenging for realised kernels. They are when there are local trends in the
data, over periods of around 10 minutes, where the prices and quotes are driven
up or down. These can be associated with high volumes. One explanation for this
is that they are due to non-trivial liquidity effects.
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Paper
Designing realised kernels to measure the ex-post
variation of equity prices in the presence of noise
Econometrica
,
Vol. 76, No. 6 (November, 2008), 1481–1536
Abstract: This This
paper shows how to use realised kernels to carry out efficient feasible
inference on the ex-post variation of underlying equity prices in the presence
of simple models of market frictions. The weights can be chosen to achieve the
best possible rate of convergence and to have an asymptotic variance which is
close to that of the maximum likelihood estimator in the parametric version of
this problem. Realised kernels can also be selected to (i) be analysed using
endogenously spaced data such as that in databases on transactions, (ii) allow
for market frictions which are endogenous, (iii) allow for temporally dependent
noise. The finite sample performance of our estimators is studied using
simulation, while empirical work illustrates their use in practice.
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Working paper
version Published
version
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Simulation
appendix
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Empirical
appendix: Description of data and estimations
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Empirical
appendix: Tables and plots for 2004
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Empirical
appendix: Tables and plots for 2000
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Code in Ox
Subsampling
Realised Kernels
Forthcoming in Journal of
Econometrics
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..
Downloads
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Paper
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For a description
of the data see the corresponding appendix for the paper: Designing realised kernels to measure the ex-post variation of equity
prices in the presence of noise
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Empirical appendix: Description of estimations
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Empirical appendix: Tables and plots for
2004
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Empirical appendix: Tables and plots for 2000