Interpretation of Continuous-Time Autoregressive Processes as Random Exponential Splines

We consider the class of continuous-time autoregressive (CAR) processes driven by (possibly non-Gaussian) Lévy white noises. When the excitation is an impulsive noise, also known as compound Poisson noise, the associated CAR process is a random non-uniform exponential spline. Therefore, Poisson-type processes are relatively easy to understand in the sense that they have a finite rate of innovation. We show in this paper that any CAR process is the limit in distribution of a sequence of CAR processes driven by impulsive noises. Hence, we provide a new interpretation of general CAR processes as limits of random exponential splines. We illustrate our result with simulations.


Published in:
Proceedings of the Eleventh International Workshop on Sampling Theory and Applications (SampTA'15), Washington DC, USA, 231–235
Year:
2015
Publisher:
IEEE
Laboratories:




 Record created 2015-09-18, last modified 2018-03-17

External links:
Download fulltextURL
Download fulltextURL
Download fulltextURL
Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)