Sampling, Embedding and Inference for CARMA Processes

A CARMA(p,q) process Y is a strictly stationary solution Y of the pth‐order formal stochastic differential equation a(D)Yt = b(D)DLt, where L is a two‐sided Levy process, a(z) and b(z) are polynomials of degrees p and q respectively, with p > q, and D denotes differentiation with respect to t. Since estimation of the coefficients of a(z) and b(z) is frequently based on observations of the Δ‐sampled sequence YΔ:=(YnΔ)n∈Z, for some Δ > 0, it is crucial to understand the relation between Y and YΔ. If EL12