Journal article
A note on non-negative continuous time processes
Journal of the Royal Statistical Society. Series B, Statistical methodology, Vol.67(4), pp.589-597
2005
DOI: 10.1111/j.1467-9868.2005.00517.x
Abstract
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. © 2005 Royal Statistical Society.
Details
- Title: Subtitle
- A note on non-negative continuous time processes
- Creators
- Henghsiu Tsai - Academia SinicaK. S Chan - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of the Royal Statistical Society. Series B, Statistical methodology, Vol.67(4), pp.589-597
- Publisher
- Blackwell
- DOI
- 10.1111/j.1467-9868.2005.00517.x
- ISSN
- 1369-7412
- eISSN
- 1467-9868
- Grant note
- DOI: 10.13039/501100001868, name: National Science Council, award: NSC 92-2118-M-001-018; DOI: 10.13039/100000001, name: National Science Foundation, award: DMS-0405267
- Language
- English
- Date published
- 2005
- Academic Unit
- Statistics and Actuarial Science; Radiology
- Record Identifier
- 9984257633102771
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