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A Note on the Non-negativity of Continuous-time ARMA and GARCH Processes. (2006)
| Citations: | 5 - 0 self |
BibTeX
@TECHREPORT{Tsai06anote,
author = {Henghsiu Tsai and Kung-Sik Chan},
title = {A Note on the Non-negativity of Continuous-time ARMA and GARCH Processes.},
institution = {},
year = {2006}
}
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Abstract
Abstract. A general approach for modeling the volatility process in continuous-time is based on the convolution of a kernel with a non-decreasing Lévy process, which is non-negative if the kernel is non-negative. Within the framework of Continuous-time Auto-Regressive Moving-Average (CARMA) processes, we derive a necessary condition for the kernel to be non-negative, and propose a numerical method for checking the non-negativity of a kernel function. These results can be lifted to solving a similar problem with another approach to modeling volatility via the COntinuous-time Generalized AutoRegressive Conditional Heteroscedastic (COGARCH) processes.
