Exponential bounds for intensity of jumps

In this paper, we study intensity of jumps in the context of functional linear processes. The natural space for that is the space D = D [0, 1] of cadlag real functions. We begin with limit theorems for ARMA D (1,1) processes. It appears that under some conditions, the functional linear process and i...

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Bibliographic Details
Published in:Mathematical methods of statistics 2014-10, Vol.23 (4), p.239-255
Main Authors: Blanke, D., Bosq, D.
Format: Article
Language:English
Subjects:
Mathematical models
Mathematics
Mathematics and Statistics
Random variables
Statistical methods
Statistical Theory and Methods
Statistics
Studies
Theorems
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Summary:In this paper, we study intensity of jumps in the context of functional linear processes. The natural space for that is the space D = D [0, 1] of cadlag real functions. We begin with limit theorems for ARMA D (1,1) processes. It appears that under some conditions, the functional linear process and its innovation have the same jumps. This nice property allows us to focus on the case of i.i.d. D -valued random variables. For such variables, we estimate the intensity of jumps in various situations: fixed number of jumps, random instants of jumps, random number of instants of jumps, etc. We derive exponential rates and limits in distribution.
ISSN:1066-5307
1934-8045
DOI:10.3103/S1066530714040012