Uniform convergence of the empirical spectral distribution function

DOI10.1016/S0304-4149(97)00053-7zbMath0913.60032OpenAlexW1981177491MaRDI QIDQ1275954

Rimas Norvaiša, Thomas Mikosch

Publication date: 14 January 1999

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

Full work available at URL: https://doi.org/10.1016/s0304-4149(97)00053-7

zbMATH Keywords

linear processperiodogramstationary processuniform law of large numbersuniform central limit theoremempirical spectral distribution function

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Stationary stochastic processes (60G10) Inference from stochastic processes and spectral analysis (62M15) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17) Probability theory on linear topological spaces (60B11)

Related Items (9)

Whittle estimation for continuous-time stationary state space models with finite second moments ⋮ Empirical spectral processes for locally stationary time series ⋮ The integrated periodogram for long-memory processes with finite or infinite variance ⋮ Weak convergence of the function-indexed integrated periodogram for infinite variance processes ⋮ Monotone spectral density estimation ⋮ The periodogram at the Fourier frequencies ⋮ Uniform limit theorems for the integrated periodogram of weakly dependent time series and their applications to Whittle's estimate ⋮ Empirical spectral processes for stationary state space models ⋮ The integrated copula spectrum

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