How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?

In this paper, we are interested in testing whether the volatility process is constant or not during a given time span by using high‐frequency data with the presence of jumps and market microstructure noise. Based on estimators of integrated volatility and spot volatility, we propose a nonparametric procedure to depict the discrepancy between local variation and global variation. We show that our proposed test statistic converges to a standard normal distribution if the volatility is constant, and diverges to infinity otherwise. Simulation studies verify the theoretical results and show a good finite sample performance of the test procedure. We also apply our test procedure to some real high‐frequency financial datasets. We observe that in almost half of the days tested, the assumption of constant volatility within a day is violated. And this is due to that the stock prices in the periods near the opening and closing are highly volatile and account for a relatively large proportion of intraday variation.

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“…A time‐varying version of

r (x)

(may be stochastic) is considered in Reference 19. The specific setting of the parameters c and

ω

are also discussed in Reference 29, supported by a great deal of simulation studies.…”

Section: Theoretical Resultsmentioning

confidence: 99%

Heteroscedasticity test of high‐frequency data with jumps and market microstructure noise

Liu

Zhi

Zhang

2022

Appl Stoch Models Bus & Ind

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“…Furthermore, Aït-Sahalia and Jacod (2009b) point out that the value of c should be proportional to the "average" value of σ t , which could be consistently estimated by the multi-power variation estimator mentioned above. The specific setting of the parameters c and ω are also discussed in Veraart (2011), supported by a great deal of simulation studies.…”

Section: Finite Activity Jumpmentioning

confidence: 99%

“…Indeed, the realised multi-power variation estimator is mainly biased by large jumps but is less affected by small jumps, while on the contrary, the truncated realised volatility is problematic in removing small jumps but eliminates large jumps effectively. In Veraart (2011), the properties of these two estimators are analyzed and compared comprehensively, their finite sample performances are verified by numerous Monte Carlo studies under different models. Furthermore, a combination of these two estimators breeds a new estimator called truncated realized multi-power variation estimator therein, which achieves the best effect of finite sample performance, since such a combination compensates the weaknesses of these two estimators.…”

Section: Finite Activity Jumpmentioning

confidence: 99%

On high frequency financial data with jumps and microstructure noise

Liu¹

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In this paper, we are interested in testing if the volatility process is constant or not during a given time span by using high-frequency data with the presence of jumps and microstructure noise. Based on estimators of integrated volatility and spot volatility, we propose a nonparametric way to depict the discrepancy between local variation and global variation. We show that our proposed test estimator converges to a standard normal distribution if the volatility is constant, otherwise it diverges to infinity. Simulation studies verify the theoretical results and show a good finite sample performance of the test procedure. We also apply our test procedure to do the heteroscedasticity test for some real high-frequency financial data. We observe that in almost half of the days tested, the assumption of constant volatility within a day is violated. And this is due to that the stock prices during opening and closing periods are highly volatile and account for a relative large proportion of intraday variation.

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On the Estimation of Integrated Volatility With Jumps and Microstructure Noise

Jing¹,

Li²,

Kong³

2014

Journal of Business & Economic Statistics

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How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?

Abstract: Realised variance, Realised multipower variation, Truncated realised variance, Inference, Stochastic volatility, Jumps,

Cited by 5 publications

References 51 publications

Heteroscedasticity test of high‐frequency data with jumps and market microstructure noise

Heteroscedasticity test of high‐frequency data with jumps and market microstructure noise

On high frequency financial data with jumps and microstructure noise

On the Estimation of Integrated Volatility With Jumps and Microstructure Noise

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