A note on non‐negative continuous time processes

Henghsiu Tsai () and K. S. Chan

Journal of the Royal Statistical Society Series B, 2005, vol. 67, issue 4, 589-597

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.

Date: 2005
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