A note on non-negative continuous time processes |
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Authors: | Henghsiu Tsai K S Chan |
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Institution: | Academia Sinica, Taipei, Republic of China; University of Iowa, Iowa City, USA |
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Abstract: | Summary. Recently there has been much work on developing models that are suitable for analysing the volatility of a continuous time process. One general approach is to define a volatility process as 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 time continuous autoregressive moving average (CARMA) processes, we derive a necessary and sufficient condition for the kernel to be non-negative. This condition is in terms of the Laplace transform of the CARMA kernel, which has a simple form. We discuss some useful consequences of this result and delineate the parametric region of stationarity and non-negative kernel for some lower order CARMA models. |
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Keywords: | Complete monotonicity Continuous time autoregressive moving average process Laplace transform Lévy process Stochastic volatility |
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