منابع مشابه
Prediction of Lévy-driven CARMA processes
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. Conditions are also established under which the...
متن کاملExistence and Uniqueness of Stationary Lévy-driven CARMA Processes
Necessary and sufficient conditions for the existence of a strictly stationary solution of the equations defining a general Lévy-driven continuous-parameter ARMA process with index set R are determined. Under these conditions the solution is shown to be unique and an explicit expression is given for the process as an integral with respect to the background driving Lévy process. The results gene...
متن کاملParametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations
We consider the parametric estimation of the driving Lévy process of a multivariate continuous-time autoregressive moving average (MCARMA) process, which is observed on the discrete time grid (0, h, 2h, . . .). Beginning with a new state space representation, we develop a method to recover the driving Lévy process exactly from a continuous record of the observed MCARMA process. We use tools fro...
متن کاملCARMA processes as solutions of integral equations
A CARMA(p, q) process is defined by suitable interpretation of the formal p order differential equation a(D)Yt = b(D)DLt, where L is a two-sided Lévy process, a(z) and b(z) are polynomials of degrees p and q, respectively, with p > q, and D denotes the differentiation operator. Since derivatives of Lévy processes do not exist in the usual sense, the rigorous definition of a CARMA process is bas...
متن کاملBasics of Lévy Processes *
This is a draft Chapter from a book by the authors on “Lévy Driven Volatility Models”.
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ژورنال
عنوان ژورنال: Journal of Econometrics
سال: 2015
ISSN: 0304-4076
DOI: 10.1016/j.jeconom.2015.03.021