期刊名称：SORT-Statistics and Operations Research Transactions
印刷版ISSN：2013-8830
出版年度：2016
卷号：1
期号：2
页码：267-302
语种：English
出版社：SORT- Statistics and Operations Research Transactions
摘要：We present a construction of a family of continuous-time ARMA processes based on p iterations of the linear operator that maps a Lévy process onto an Ornstein-Uhlenbeck process. The construction resembles the procedure to build an AR( p ) from an AR(1). We show that this family is in fact a subfamily of the well-known CARMA( p , q ) processes, with several interesting advantages, including a smaller number of parameters. The resulting processes are linear combinations of Ornstein-Uhlenbeck processes all driven by the same Lévy process. This provides a straightforward computation of covariances, a state-space model representation and methods for estimating parameters. Furthermore, the discrete and equally spaced sampling of the process turns to be an ARMA( p , p −1) process. We propose methods for estimating the parameters of the iterated Ornstein-Uhlenbeck process when the noise is either driven by a Wiener or a more general Lévy process, and show simulations and applications to real data.
关键词：Ornstein-Uhlenbeck process, Lévy process, Continuous ARMA, stationary process
