We present a new construction of continuous ARMA processes based on iterating an Ornstein–Uhlenbeck operator OUκ that maps a random variable y(t) onto OUκy(t)=∫t−∞e−κ(t−s)dy(s). This construction resembles the procedure to build an AR( p) from an AR(1) and derives in a parsimonious model for continuous autoregression, with fewer parameters to compute than the known CARMA obtained as a solution of a system of stochastic differential equations. We show properties of this operator, give state space representation of the iterated Ornstein–Uhlenbeck process and show how to estimate the parameters of the model.