A note on non-negative continuous time processes

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 67, Issue 4, 2005, Pages 589-597

  Tsai, Henghsiu ^a,c   Chan, K S ^b  

^a ACADEMIA SINICA   (Taiwan)

^b UNIVERSITY OF IOWA   (United States)

^c INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

Author keywords

Complete monotonicity; Continuous time autoregressive moving average process; Laplace transform; L vy process; Stochastic volatility

Indexed keywords

EID: 25144437396     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2005.00517.x     Document Type: Article

References (15)

1. Abramowitz, M. and Stegun, I. A. (eds) (1965) Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables. New York: Dover Publications.
2. Andersen, T. G. and Lund, J. (1997) Estimating continuous-time stochastic volatility models of the short-term interest rate. J. Econometr., 77, 343-377.
3. Ball, K. (1994) Completely monotonic rational functions and Hall's marriage theorem. J. Combin. Theory B, 61, 118-124.
4. Barndorff-Nielsen, O. E. and Shephard, N. (2001) Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics (with discussion). J. R. Statist. Soc. B, 63, 167-241.
5. Bertoin, J. (1996) Lévy Processes. Cambridge: Cambridge University Press.
6. Brockwell, P. J. (2000) Heavy-tailed and non-linear continuous-time ARMA models for financial time series. In Statistics and Finance: an Interface (eds W. S. Chan, W. K. Li and H. Tong), pp. 3-22. London: Imperial College Press.
7. Brockwell, P. J. (2001) Lévy-driven CARMA processes. Ann. Inst. Statist. Math., 53, 113-124.
8. Brockwell, P. J. (2004) Representations of continuous-time ARMA processes. J. Appl. Probab. A, 41, 375-382.
9. Brockwell, P. J. and Marquardt, T. (2005) Lévy-driven and fractionally integrated ARMA processes with continuous time parameter. Statist. Sin., 15, 477-494.
10. Comte, F. and Renault, E. (1998) Long memory in continuous-time stochastic volatility models. Math. Finan., 8, 291-323.
11. Feller, W. (1971) An Introduction to Probability Theory and Its Applications, vol. 2. New York: Wiley.
12. Klüppelberg, C., Lindner, A. and Maller, R. (2004) A continuous time GARCH process driven by a Lévy process: stationarity and second order behaviour. J. Appl. Probab., 41, 601-622.
13. Protter, P. (1991) Stochastic Integration and Differential Equations. New York: Springer.
14. Roberts, G. O., Papaspiliopoulos, O. and Dellaportas, P. (2004) Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes. J. R. Statist. Soc. B, 66, 369-393.
15. Sato, K. (1999) Lévy Processes and Infinitely Divisible Distributions. Cambridge: Cambridge University Press.