 A CLT for martingale transforms with infinite varianceStelios Arvanitis and Alexandros Louka Statistics & Probability Letters, 2016, vol. 119, issue C, 116-123 Abstract: We provide a CLT for martingale transforms that holds even when the second moments are infinite. Compared to an analogous result in Hall and Yao (2003) we impose minimal assumptions and utilize the Principle of Conditioning to verify a modified version of Lindeberg’s condition. When the variance is infinite, the rate of convergence, which we allow to be matrix valued, is slower than n and depends on the rate of divergence of the truncated second moments. In many cases it can be consistently estimated. A major application concerns the characterization of the rate and the limiting distribution of the Gaussian QMLE in the case of GARCH type models with infinite fourth moments for the innovation process. The results are particularly useful in the case of the EGARCH(1,1) model as we show that the usual limit theory is still valid without any further parameter restrictions when we relax the assumption for finite fourth moments of the innovation process. Keywords: CLT; Generalized domain of attraction; Martingale transform; Matrix normalization; Self-normalized wald tests; QMLE (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:119:y:2016:i:c:p:116-123 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spl.2016.07.015 Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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