# Rate-optimal tests for jumps in diffusion processes

## Author Info

Listed author(s):
• Taesuk Lee
• Mico Loretan
• Werner Ploberger

()

Registered author(s):

## Abstract

Suppose one has a sample of high-frequency intraday discrete observations of a continuous time random process, such as foreign exchange rates and stock prices, and wants to test for the presence of jumps in the process. We show that the power of any test of this hypothesis depends on the frequency of observation. In particular, if the process is observed at intervals of length $$1/n$$ 1 / n and the instantaneous volatility of the process is given by $$\sigma _{t}$$ σ t , we show that at best one can detect jumps of height no smaller than $$\sigma _{t}\sqrt{2\log (n)/n}$$ σ t 2 log ( n ) / n . We present a new test which achieves this rate for diffusion-type processes, and examine its finite-sample properties using simulations. Copyright Springer-Verlag Berlin Heidelberg 2013

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File URL: http://hdl.handle.net/10.1007/s00362-013-0541-y

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## Bibliographic Info

Article provided by Springer in its journal Statistical Papers.

Volume (Year): 54 (2013)
Issue (Month): 4 (November)
Pages: 1009-1041

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 Handle: RePEc:spr:stpapr:v:54:y:2013:i:4:p:1009-1041 DOI: 10.1007/s00362-013-0541-y Contact details of provider: Web page: http://www.springer.com Order Information: Web: http://www.springer.com/statistics/business/journal/362

## References

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1. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
2. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
3. Chaboud, Alain P. & Chiquoine, Benjamin & Hjalmarsson, Erik & Loretan, Mico, 2010. "Frequency of observation and the estimation of integrated volatility in deep and liquid financial markets," Journal of Empirical Finance, Elsevier, vol. 17(2), pages 212-240, March.
4. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
5. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
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