Consistent estimation of covariation under nonsynchronicity

Takaki Hayashi; Shigeo Kusuoka

doi:10.1007/s11203-007-9009-9

Consistent estimation of covariation under nonsynchronicity

Takaki Hayashi, Shigeo Kusuoka

Graduate School of Business Administration

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

We present a methodology to estimate the covariance of two time series when they are sampled from continuous semimartingales at general stopping times in a nonsynchronous manner. Approximation error bounds being explored, the estimators are shown to be consistent as the size of the sampling intervals tends to zero. The methodology is easy to be implemented with potentially broad applications, especially in financial modeling and analysis involving high-frequency transaction data. The results generalize those recently obtained by obtained by Hayashi and Yoshida (2005, Bernoulli 11(2):359-379)

Original language	English
Pages (from-to)	93-106
Number of pages	14
Journal	Statistical Inference for Stochastic Processes
Volume	11
Issue number	1
DOIs	https://doi.org/10.1007/s11203-007-9009-9
Publication status	Published - 2008 Feb

Keywords

Consistency
Discrete-time sampling
High-frequency data
Nonsynchronous trading
Quadratic variation
Realized covariance
Semimartingale
Stopping time

ASJC Scopus subject areas

Statistics and Probability

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10.1007/s11203-007-9009-9

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abstract = "We present a methodology to estimate the covariance of two time series when they are sampled from continuous semimartingales at general stopping times in a nonsynchronous manner. Approximation error bounds being explored, the estimators are shown to be consistent as the size of the sampling intervals tends to zero. The methodology is easy to be implemented with potentially broad applications, especially in financial modeling and analysis involving high-frequency transaction data. The results generalize those recently obtained by obtained by Hayashi and Yoshida (2005, Bernoulli 11(2):359-379)",

keywords = "Consistency, Discrete-time sampling, High-frequency data, Nonsynchronous trading, Quadratic variation, Realized covariance, Semimartingale, Stopping time",

author = "Takaki Hayashi and Shigeo Kusuoka",

note = "Funding Information: Acknowledgements The authors are grateful to Professors Jean Jacod, Masaaki Kijima, and Per Mykland for their useful comments. The authors are especially indebted to Professor Nakahiro Yoshida for his valuable suggestions. Most of the work was done during the first author{\textquoteright}s stay at the University of Tokyo, Graduate School of Mathematical Sciences, in the spring and summer of 2004, which led to the previous vesion of the paper, Hayashi and Kusuoka (2004). He wishes to thank the school for its hospitality. He gratefully acknowledges financial support from the 21st Century COE Program at Graduate School of Mathematical Sciences, the",

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AU - Kusuoka, Shigeo

N1 - Funding Information: Acknowledgements The authors are grateful to Professors Jean Jacod, Masaaki Kijima, and Per Mykland for their useful comments. The authors are especially indebted to Professor Nakahiro Yoshida for his valuable suggestions. Most of the work was done during the first author’s stay at the University of Tokyo, Graduate School of Mathematical Sciences, in the spring and summer of 2004, which led to the previous vesion of the paper, Hayashi and Kusuoka (2004). He wishes to thank the school for its hospitality. He gratefully acknowledges financial support from the 21st Century COE Program at Graduate School of Mathematical Sciences, the

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N2 - We present a methodology to estimate the covariance of two time series when they are sampled from continuous semimartingales at general stopping times in a nonsynchronous manner. Approximation error bounds being explored, the estimators are shown to be consistent as the size of the sampling intervals tends to zero. The methodology is easy to be implemented with potentially broad applications, especially in financial modeling and analysis involving high-frequency transaction data. The results generalize those recently obtained by obtained by Hayashi and Yoshida (2005, Bernoulli 11(2):359-379)

AB - We present a methodology to estimate the covariance of two time series when they are sampled from continuous semimartingales at general stopping times in a nonsynchronous manner. Approximation error bounds being explored, the estimators are shown to be consistent as the size of the sampling intervals tends to zero. The methodology is easy to be implemented with potentially broad applications, especially in financial modeling and analysis involving high-frequency transaction data. The results generalize those recently obtained by obtained by Hayashi and Yoshida (2005, Bernoulli 11(2):359-379)

KW - Consistency

KW - Discrete-time sampling

KW - High-frequency data

KW - Nonsynchronous trading

KW - Quadratic variation

KW - Realized covariance

KW - Semimartingale

KW - Stopping time

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Consistent estimation of covariation under nonsynchronicity

Abstract

Keywords

ASJC Scopus subject areas

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