A minimal contrast estimator for the linear fractional stable motion

Mathias Mørck Ljungdahl () and Mark Podolskij ()
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Mathias Mørck Ljungdahl: Aarhus University
Mark Podolskij: Aarhus University

Statistical Inference for Stochastic Processes, 2020, vol. 23, issue 2, No 7, 413 pages

Abstract: Abstract In this paper we present an estimator for the three-dimensional parameter $$(\sigma , \alpha , H)$$ ( σ , α , H ) of the linear fractional stable motion, where H represents the self-similarity parameter, and $$(\sigma , \alpha )$$ ( σ , α ) are the scaling and stability parameters of the driving symmetric Lévy process L. Our approach is based upon a minimal contrast method associated with the empirical characteristic function combined with a ratio type estimator for the self-similarity parameter H. The main result investigates the strong consistency and weak limit theorems for the resulting estimator. Furthermore, we propose several ideas to obtain feasible confidence regions in various parameter settings. Our work is mainly related to Ljungdahl and Podolskij (A note on parametric estimation of Lévy moving average processes, p 294, 2019) and Mazur et al. (Bernoulli 26(1): 226–252, 2020) in which parameter estimation for the linear fractional stable motion and related Lévy moving average processes has been studied.

Keywords: Linear fractional processes; Lévy processes; Limit theorems; Parametric estimation; Bootstrap; Subsampling; Self-similarity; Low frequency; Primary 60G22; 62F12; 62E20; Secondary 60E07; 60F05; 60G10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11203-020-09216-2

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