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Title: On modelling and estimation of stationary processes Authors:  Marko Voutilainen - Aalto University (Finland) [presenting]
Abstract: Stationary processes form an important class of stochastic processes that has been extensively studied in the literature. Their applications include modelling and forecasting numerous real-life phenomenon including natural disasters, sustainable energy sources, sales and market movements. We present a novel way for modelling and estimating $n$-dimensional strictly stationary processes, both in discrete and continuous time. The approach is based on the observation that stationary processes are characterized by an AR(1) type of (matrix) equation in discrete time, and by n-dimensional Langevin equation in continuous time. As a consequence, we obtain a continuous time algebraic Riccati equation for the model parameter matrix given by the characterization. The Riccati equation provides us with a natural estimator of the model parameter that inherits consistency and asymptotic properties from the autocovariance function of the stationary process.