Invariance principles for some FARIMA and nonstationary linear processes in the domain of a stable distribution

2010/07/04 by Ph. Barbe, Barbe, Ph., William P. McCormick +2
Economics, Econometrics and Finance · Mathematics · #60F17 (Primary) 60G22 #60G50 #60G52 #60G55 #62G32 (Secondary) #62M10 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistical Distribution Estimation and Applications #Stochastic processes and financial applications #math.PR #msc:60F17 #msc:60G22 #msc:60G50 #msc:60G52 #msc:60G55 #msc:62G32 #msc:62M10

paper · pdf · doi:10.48550/arxiv.1007.0576

77 pages, 1 figure

arxiv created 2010/07/04 · openalex publication_date 2010/07/04 · arxiv updated 2010/07/06 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We prove some invariance principles for processes which generalize FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution. The limiting processes are extensions of the fractional Lévy processes. The technique used is interesting in itself; it extends an older idea of splitting a sample into a central part and an extreme one, analyzing each part with different techniques, and then combining the results. This technique seems to have the potential to be useful in other problems in the domain of nonGaussian stable distributions.

Citations

• Convergence of Random Processes and Limit Theorems in Probability Theory
• Veraverbeke's theorem at large - On the maximum of some processes with negative drift and heavy tail innovations

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