Prediction of Lévy-driven CARMA processes

Abstract

The conditional expectations, E(Y (h)|Y (u),−∞ < u ≤ 0) and E(Y (h)|Y (u),−M ≤ u ≤ 0) with h > 0 and 0 < M < ∞ are determined for a continuous-time ARMA (CARMA) process (Y (t))t∈R driven by a Lévy process L with E|L(1)| < ∞. If E(L(1)2) <∞ these are the minimum mean-squared error predictors of Y (h) given (Y (t))t≤0 and (Y (t))−M≤t≤0 respectively… (More)

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