Abstract
We explain the connection between autocorrelation functions of stationary continuous time processes and real characteristic functions, and review sufficient conditions for a function to be an autocorrelation function. We also give probabilistic constructions for time series reformulations of Theorem on characteristic functions, and classical theorem in Fourier analysis. Our constructions allow the marginal distribution of the process to be any infinitely divisible distribution with finite variance.
Original language | English |
---|---|
Pages (from-to) | 255-271 |
Number of pages | 17 |
Journal | International Statistical Review |
Volume | 79 |
Issue number | 2 |
DOIs | |
Publication status | Published - Aug 2011 |