In this paper, we study new definitions of noncausality, set in a continuous time framework, illustrated by the intuitive example of stochastic volatility models. Then, we define CIMA processes (i.e., processes admitting a continuous time invertible moving average representation), for which...

We consider a model <italic>Y</italic>_null = σ_nullη_null in which (σ_null) is not independent of the noise process (η_null) but σ_null is independent of η_null for each <italic>t</italic>. We assume that (σ_null) is stationary, and we propose an adaptive estimator of the density of ln(σ_null²) based on the observations <italic>Y</italic>_null....