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 Lévy 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. Si...

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Bibliographic Details
Published in:Journal of time series analysis 2019-03, Vol.40 (2), p.163-181
Main Authors: Brockwell, Peter J., Lindner, Alexander
Format: Article
Language:English
Subjects:
CARMA process
Coefficients
complex‐valued information matrix
Differential equations
Differentiation
Embedding
Polynomials
quasi‐maximum‐likelihood estimation
Sampling
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Summary: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 Lévy 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
ISSN:0143-9782
1467-9892
DOI:10.1111/jtsa.12433