Approximate self-weighted LAD estimation of discretely observed ergodic Ornstein-Uhlenbeck processes
By Hiroki Masuda. 2010
54 citations recorded by the source corpus.
We consider drift estimation of a discretely observed Ornstein-Uhlenbeck process driven by a possibly heavy-tailed symmetric Levy process with positive BlumenthalGetoor activity index β. Under an infill and large-time sampling design, we first establish an asymptotic normality of a self-weighted least absolute deviation estimator with the rate of convergence being √ nh 1−1/β n , where n denotes sample size and hn > 0 the sampling mesh satisfying that hn → 0 and nhn → ∞. This implies that the rate of convergence is determined by the most active part of the driving Levy process; the presence of a driving Wiener part leads to √ nhn, which is familiar in the context of asymptotically efficient estimation of diffusions with compound Poisson jumps, while a pure-jump driving Levy process leads to a faster one. Also discussed is how to construct corresponding asymptotic confidence regions without full specification of the driving Levy process. Second, by means of a polynomial type large deviation inequality we derive convergence of moments of our estimator under additional conditions.
Subfields: Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/b78df541e9fe8cdb633df764becc379ee4ad88e3
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Citations in the corpus
- Convergence of Gaussian quasi-likelihood random fields for ergodic Lévy driven SDE observed at high frequency (2013, background): “We refer to Kulik [19, 20], Maruyama and Tanaka [26], Menaldi and Robin [33], Meyn and Tweedie [34] and Wang [45] as well as Masuda [28, 29] for some general results concerning the (exponential) ergodicity.”