The integrated periodogram for long-memory processes with finite or infinite variance

DOI10.1016/S0304-4149(96)00124-XzbMath0885.62108MaRDI QIDQ1382496

Piotr S. Kokoszka, Thomas Mikosch

Publication date: 29 March 1998

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

zbMATH Keywords

functional limit theoremsgoodness-of-fit testsheavy tailslong-memoryintegrated periodogramfractional ARIMA

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Inference from stochastic processes and spectral analysis (62M15) Functional limit theorems; invariance principles (60F17)

Related Items (18)

Bootstrap specification tests for linear covariance stationary processes ⋮ Record length requirement of long-range dependent teletraffic ⋮ Discriminating between long-range dependence and non-stationarity ⋮ Approximations and limit theory for quadratic forms of linear processes ⋮ The asymptotic behavior of quadratic forms in heavy-tailed strongly dependent random variables ⋮ Weak convergence of the function-indexed integrated periodogram for infinite variance processes ⋮ The periodogram at the Fourier frequencies ⋮ Weak convergence of multivariate fractional processes ⋮ On \(1/f\) noise ⋮ IMPULSE RESPONSES OF FRACTIONALLY INTEGRATED PROCESSES WITH LONG MEMORY ⋮ Semi-parametric estimation of long-range dependence index in infinite variance time series. ⋮ Stable limits of empirical processes of moving averages with infinite variance. ⋮ The asymptotic behavior of quadratic forms in \(\varphi\)-mixing random variables ⋮ Uniform convergence of the empirical spectral distribution function ⋮ Long range dependence for stable random processes ⋮ Local empirical spectral measure of multivariate processes with long range dependence. ⋮ Empirical spectral processes for stationary state space models ⋮ The integrated copula spectrum

Uses Software

• longmemo

Cites Work

• The effect of long-range dependence on change-point estimators
• Goodness of fit tests for spectral distributions
• Functional limit theorems for random quadratic forms
• Limit theory for moving averages of random variables with regularly varying tail probabilities
• Asymptotic normality of spectral estimates
• Decoupling inequalities for multilinear forms in independent symmetric random variables
• Limit theory for the sample covariance and correlation functions of moving averages
• Empirical spectral processes and their applications to time series analysis
• Functional CLT for nonparametric estimates of the spectrum and change- point problem for a spectral function
• Time series: theory and methods.
• Uniform convergence of the empirical spectral distribution function
• Testing and estimating in the change-point problem of the spectral function
• The integrated periodogram for stable processes
• Parameter estimation for infinite variance fractional ARIMA
• Discrete time parametric models with long memory and infinite variance
• Parameter estimation for ARMA models with infinite variance innovations
• Fractional ARIMA with stable innovations
• The change-point problem for dependent observations
• Gaussian limit fields for the integrated periodogram
• Multilinear forms in Pareto-like random variables and product random measures
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