A continuous-time framework for ARMA processes Article Swipe

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Andreas Basse-O’Connor , Mikkel Slot Nielsen , Jan Skov Pedersen , Victor Rohde ·

YOU? · · 2017 · Open Access · · OA: W2611680109

Based on a vast literature on continuous-time moving average processes we suggest an analogue for an autoregressive structure, and from this we combine the two concepts to a model for stationary processes which exhibit an ARMA type behavior. We relate this framework to CARMA processes, and thereby shed light on new aspects of these well-studied processes. Within the model we obtain existence and uniqueness results and study the structure of the solution process. Solutions to general stochastic delay differential equations constitute a particular subclass of these ARMA type processes, and we study these in detail. The results obtained for this subclass go beyond already existing literature.