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A minimal contrast estimator for the linear fractional stable motion

Author

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  • Mathias Mørck Ljungdahl

    (Aarhus University)

  • Mark Podolskij

    (Aarhus University)

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.

Suggested Citation

  • Mathias Mørck Ljungdahl & Mark Podolskij, 2020. "A minimal contrast estimator for the linear fractional stable motion," Statistical Inference for Stochastic Processes, Springer, vol. 23(2), pages 381-413, July.
    • Handle: RePEc:spr:sistpr:v:23:y:2020:i:2:d:10.1007_s11203-020-09216-2
    DOI: 10.1007/s11203-020-09216-2
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    Cited by:

    1. Mathias Mørck Ljungdahl & Mark Podolskij, 2022. "Multidimensional parameter estimation of heavy‐tailed moving averages," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 593-624, June.
    2. Azmoodeh, Ehsan & Ljungdahl, Mathias Mørck & Thäle, Christoph, 2022. "Multi-dimensional normal approximation of heavy-tailed moving averages," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 308-334.

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