Limit Theorems for Moving Averages with Random Coefficients and Heavy-Tailed Noise

DOI10.1239/jap/1143936257zbMath1097.62082OpenAlexW2048851037MaRDI QIDQ5489003

Rafał Kulik

Publication date: 25 September 2006

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jap/1143936257

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (14)

Maxima of linear processes with heavy‐tailed innovations and random coefficients ⋮ Regular Variation of Infinite Series of Processes with Random Coefficients ⋮ Convergence rates in the law of large numbers for END linear processes with random coefficients ⋮ Limiting behaviors of linear processes with random coefficients based on m-ANA random variables ⋮ A functional limit theorem for self-normalized linear processes with random coefficients and i.i.d. heavy-tailed innovations ⋮ Convergence of asymptotically almost negatively associated random variables with random coefficients ⋮ Asymptotic properties of the tail distribution and Hill's estimator for shot noise sequence ⋮ Unnamed Item ⋮ Complete moment convergence for the dependent linear processes with random coefficients ⋮ Topological crackle of heavy-tailed moving average processes ⋮ Limiting behavior of randomly weighted averages of symmetric heavy-tailed random variables ⋮ Functional convergence for moving averages with heavy tails and random coefficients ⋮ A functional limit theorem for moving averages with weakly dependent heavy-tailed innovations ⋮ Convergence of point processes with weakly dependent points

Cites Work

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• Implicit renewal theory and tails of solutions of random equations
• Limit theory for moving averages of random variables with regularly varying tail probabilities
• Extremes of moving averages of random variables from the domain of attraction of the double exponential distribution
• Strict stationarity of generalized autoregressive processes
• Limit theory for bilinear processes with heavy-tailed noise
• Poisson limits for \(U\)-statistics.
• The sample autocorrelations of heavy-tailed processes with applications to ARCH
• Point process and partial sum convergence for weakly dependent random variables with infinite variance
• Large deviations and ruin probabilities for solutions to stochastic recurrence equations with heavy-tailed innovations
• Moving averages with random coefficients and random coefficient autoregressive models
• A test for nonlinearity of time series with infinite variance

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