JSM 2005 - Toronto

Abstract #303059

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Activity Number: 141
Type: Contributed
Date/Time: Monday, August 8, 2005 : 10:30 AM to 12:20 PM
Sponsor: General Methodology
Abstract - #303059
Title: A Note on Nonnegative Continuous-time Processes
Author(s): Henghsiu Tsai*+ and Kung-Sik Chan
Companies: Institute of Statistical Science, Academia Sinica and The University of Iowa
Address: Institute of Statistical Science, Taipei, 115, Taiwan
Keywords: completely monotone ; continuous-time ARMA process ; Levy process ; Laplace transform ; stochastic volatility
Abstract:

Recently, there are many works on developing models suitable for analyzing the volatility of a continuous-time process. One general approach is to define a volatility process as the convolution of a kernel with a nondecreasing Levy process---which is nonnegative if the kernel is nonnegative. Within the framework of Continuous-time Auto-Regressive Moving-Average (CARMA) processes, we derive a necessary and sufficient condition for the kernel to be nonnegative. This condition is in terms of the Laplace transform of the CARMA kernel, which has a simple form. We discuss useful consequences of this result and delineate the parametric region of stationarity and nonnegative kernel for lower-order CARMA models.

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