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ESTIMATION AND INFERENCE FOR MULTIVARIATE CONTINUOUS-TIME AUTOREGRESSIVE PROCESSES
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DOI：10.1214/25-AAP2244.png)
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Abstract
En 中文
The aim of this paper is to develop estimation and inference methods for the drift parameters of multivariate L & eacute;vy-driven continuous-time autoregressive processes of order p is an element of N. Starting from a continuous-time observation of the process, we develop consistent and asymptotically normal maximum likelihood estimators. We then relax the unrealistic assumption of continuous-time observation by considering natural discretizations based on a combination of Riemann-sum, finite difference, and thresholding approximations. The resulting estimators are also proven to be consistent and asymptotically normal under a general set of conditions, allowing for both finite and infinite jump activity in the driving L & eacute;vy process. When discretizing the estimators, allowing for irregularly spaced observations is of great practical importance. In this respect, CAR(p) models are not just relevant for true continuous-time processes: a CAR(p) specification provides a natural continuous-time interpolation for modeling irregularly spaced data-even if the observed process is inherently discrete. As a practically relevant application, we consider the setting where the multivariate observation is known to possess a graphical structure. We refer to such a process as GrCAR and discuss the corresponding drift estimators and their properties. The finite sample behavior of all theoretical asymptotic results is empirically assessed by extensive simulation experiments.
Keywords:
Estimation
inference
asymptotic properties
autoregressive
continuous-time
L & eacute
vy process
maximum likelihood
Ornstein-Uhlenbeck process
state-space models
graph topology
Journal
A
IF:
1.8
Papers:
84
Citations:
4.4K