Abstract
This paper is devoted to the estimation of the intensity and the density of jumps for \(D\left[ 0,1\right] \)-valued random variables and the construction of detectors for constant or random jumps. Limit theorems are obtained in the context of continuous observations or high-frequency data. Applications to jumps for \(D\left[ 0,1\right] \)-valued moving average and autoregressive processes are considered. We also study the special case where there is an infinity of jumps. Thus, our approach is somewhat different from that which consists of studying jumps in semimartingales.
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I want to thank the associate editor and the two referees for their very useful comments which allowed me to notably improve the original manuscript.
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Bosq, D. (2015). Estimating and Detecting Jumps. Applications to \(D\left[ 0,1\right] \)-Valued Linear Processes. In: Hallin, M., Mason, D., Pfeifer, D., Steinebach, J. (eds) Mathematical Statistics and Limit Theorems. Springer, Cham. https://doi.org/10.1007/978-3-319-12442-1_4
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DOI: https://doi.org/10.1007/978-3-319-12442-1_4
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