Spectral estimates and stable processes

DOI10.1016/0304-4149(93)90021-UzbMath0779.60023OpenAlexW2048291892MaRDI QIDQ689470

Claudia Klüppelberg, Thomas Mikosch

Publication date: 19 January 1994

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(93)90021-u

zbMATH Keywords

characteristic functionstable lawsmoving average processperiodogramstable processesgeneral linear modelspectral estimate

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Inference from stochastic processes and spectral analysis (62M15)

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The maximum of the periodogram for a heavy-tailed sequence. ⋮ Modelling of extremal events in insurance and finance ⋮ Fractional ARIMA with stable innovations ⋮ The divisible sandpile with heavy-tailed variables ⋮ Large sample theory for statistics of stable moving averages ⋮ Guaranteed detection of an imbalance instant of the GARCH-process ⋮ An empirical likelihood approach for symmetric \(\alpha\)-stable processes ⋮ The periodogram at the Fourier frequencies ⋮ Empirical likelihood approach toward discriminant analysis for dynamics of stable processes ⋮ Non‐stationary autoregressive processes with infinite variance ⋮ Discriminant analysis for dynamics of stable processes ⋮ Cluster Analysis for Stable Processes ⋮ Thek-factor GARMA Process with Infinite Variance Innovations ⋮ Gauss-Newton and M-estimation for ARMA processes with infinite variance ⋮ Gaussian limit fields for the integrated periodogram

Cites Work

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• Limit theory for moving averages of random variables with regularly varying tail probabilities
• Time series: theory and methods
• Limit theory for the sample covariance and correlation functions of moving averages
• Extrema of skewed stable processes
• Discrete-time stable processes and their certain properties
• A weak invariance principle with applications to domains of attraction
• Prediction of stable processes: Spectral and moving average representations
• Harmonizable stable processes
• Some Structure Theorems for the Symmetric Stable Laws

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