# Rate-optimal tests for jumps in diffusion processes

## Author

Listed:
• Taesuk Lee
• Mico Loretan
• Werner Ploberger

()

## 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

## Suggested Citation

• Taesuk Lee & Mico Loretan & Werner Ploberger, 2013. "Rate-optimal tests for jumps in diffusion processes," Statistical Papers, Springer, vol. 54(4), pages 1009-1041, November.
• Handle: RePEc:spr:stpapr:v:54:y:2013:i:4:p:1009-1041
DOI: 10.1007/s00362-013-0541-y
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File URL: http://hdl.handle.net/10.1007/s00362-013-0541-y

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## References listed on IDEAS

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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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1. repec:eee:econom:v:204:y:2018:i:2:p:248-267 is not listed on IDEAS

### Keywords

Financial econometrics; High-frequency data; Jumps; Likelihood ratio test;

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