Least Squares Inference on Integrated Volatility and the Relationship between Efficient Prices and Noise

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Least Squares Inference on Integrated Volatility and the Relationship between Efficient Prices and Noise

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Ingmar Nolte () (Warwick Business School,FERC, CoFE)
Valeri Voev () (University of Aarhus, CoFE and CREATES)

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Abstract

The expected value of sums of squared intraday returns (realized variance) gives rise to a least squares regression which adapts itself to the assumptions of the noise process and allows for a joint inference on integrated volatility (IV), noise moments and price-noise relations. In the iid noise case we derive the asymptotic variance of the regression parameter estimating the IV, show that it is consistent and compare its asymptotic efficiency against alternative consistent IV measures. In case of noise which is correlated with the efficient return process, we postulate a new “asymptotically increasing” type of dependence and analyze its ability to cope with the empirically observed price-noise dependence in quote data. In the empirical section of the paper we apply the LS methodology to estimate the integrated volatility as well as the noise properties of 25 liquid stocks both with midquote and transaction price data. We find that while iid noise is an oversimplification, its non-iid characteristics have a decidedly negligible effect on volatility estimation within our framework, for which we provide a sound theoretical reason. In terms of noise-price endogeneity, we are not able to find empirical support for simple ad hoc theoretical models and we provide an alternative explanation for the observed patterns in midquote data, based on market microstructure theory.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-16.

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Length: 40
Date of creation: 27 Apr 2009
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Handle: RePEc:aah:create:2009-16

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Find related papers by JEL classification:
G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
F31 - International Economics - - International Finance - - - Foreign Exchange
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

This paper has been announced in the following NEP Reports:

NEP-ALL-2009-05-02 (All new papers)
NEP-ECM-2009-05-02 (Econometrics)
NEP-FMK-2009-05-02 (Financial Markets)
NEP-MST-2009-05-02 (Market Microstructure)

References listed on IDEAS
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Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March. [Downloadable!] (restricted)
Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," OFRC Working Papers Series 2008fe29, Oxford Financial Research Centre. [Downloadable!]
Other versions:
- Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Multivariate realised kernels: consistent positive semin-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Economics Series Working Papers 397, University of Oxford, Department of Economics. [Downloadable!]
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- Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," CREATES Research Papers 2008-63, School of Economics and Management, University of Aarhus. [Downloadable!]
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Other versions:
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Other versions:
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Other versions:
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