Continuous-time Moving-average Processes: Modeling and Statistics
Continuous-time moving-average processes form a large class of stochastic processes containing both classical semimartingales as, for example, Ornstein-Uhlenbeck processes, and long memory processes as, for example, the fractional Brownian motion. We will investigate Lévy-driven continuous-time moving-average processes $\int f(t,s) dL_s$ which allow to connect an arbitrary correlation structure given by a kernel function $f$ with infinitely divisible marginal distributions given by the driving Lévy prozess $L$. As examples we consider fractional Lévy motions connecting long-time dependence with infinitely divisible marginal distributions and oscillating Ornstein-Uhlenbeck processes, which are promising models for the seasonalities of electricity prices. Besides discussing aspects of modeling, we derive estimation procedures for the processes and consider an empirical application to electricity data.