Adaptive prediction of non-Gaussian Ornstein-Uhlenbeck process

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.

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