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Nonparametric estimation of the kernel function of symmetric stable moving average random functions.
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- Author(s): Kampf, Jürgen; Shevchenko, Georgiy; Spodarev, Evgeny
- Source:
Annals of the Institute of Statistical Mathematics; Apr2021, Vol. 73 Issue 2, p337-367, 31p- Subject Terms:
- Source:
- Additional Information
- Abstract: We estimate the kernel function of a symmetric alpha stable ( S α S ) moving average random function which is observed on a regular grid of points. The proposed estimator relies on the empirical normalized (smoothed) periodogram. It is shown to be weakly consistent for positive definite kernel functions, when the grid mesh size tends to zero and at the same time the observation horizon tends to infinity (high-frequency observations). A simulation study shows that the estimator performs well at finite sample sizes, when the integrator measure of the moving average random function is S α S and for some other infinitely divisible integrators. [ABSTRACT FROM AUTHOR]
- Abstract: Copyright of Annals of the Institute of Statistical Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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