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Estimating the degree of activity of jumps in high frequency data. (English) Zbl 1173.62060

Summary: We define a generalized index of jump activity, propose estimators of that index for a discretely sampled process and derive the estimators’ properties. These estimators are applicable despite the presence of Brownian volatility in the process, which makes it more challenging to infer the characteristics of the small, infinite activity jumps. When the method is applied to high frequency stock returns, we find evidence of infinitely active jumps in the data and estimate their index of activity.

MSC:

62M05 Markov processes: estimation; hidden Markov models
62F12 Asymptotic properties of parametric estimators
62P05 Applications of statistics to actuarial sciences and financial mathematics
65C05 Monte Carlo methods
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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References:

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