Adaptive prediction of non-Gaussian Ornstein-Uhlenbeck process

Abstract

This paper proposes adaptive predictors of non-Gaussian Ornstein-Uhlenbeck process with unknown parameters.Predictors are based on the truncated parameter estimators.Asymptotic and non-asymptotic properties of the predictors are investigated.In particular, there is found the rate of convergence of the second moment of a prediction error to its minimum value.In addition, there is established an asymptotic optimality of the adaptive predictors in the sense of a special risk function.The structure of the risk function assumes the optimization of both the duration of observations and the prediction quality.