Detecting instants of jumps and estimating their intensity in the context of p derivatives with continuous or discrete data

ABSTRACT

In this article, we consider the ARD^(p)(1) process where D[0, 1] is the space of cadlag function and the pth derivative has a possible jump. One envisages to detect the position and intensity of jump in the context of p derivatives with continuous or discrete data. We also envisage jump for the (p + 1)th derivative. The main result allows to detect jump and to detect intensity of jump simultaneously. Asymptotic results are derived.

KEYWORDS:

• Consistency
• Continuous data
• Detecting instant of jump
• Discrete data
• Intensity of derivative
• Limit in distribution.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E20
• 62J05
• 62G08
• G2M10

Acknowledgments

I thank the referee for his detailed report which allowed me to substantially improve the presentation of the article. We would like to thank Delphine Blanke for fruitful suggestions.