A note on the non-negativity of continuous-time ARMA and GARCH processes

نویسندگان

  • Henghsiu Tsai
  • Kung-Sik Chan
چکیده

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.

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عنوان ژورنال:
  • Statistics and Computing

دوره 19  شماره 

صفحات  -

تاریخ انتشار 2009