Approximations and limit theory for quadratic forms of linear processes

DOI10.1016/j.spa.2006.05.015zbMath1107.62038OpenAlexW2058342872MaRDI QIDQ873607

R. J. Bhansali, Piotr S. Kokoszka, Liudas Giraitis

Publication date: 29 March 2007

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

Full work available at URL: https://doi.org/10.1016/j.spa.2006.05.015

zbMATH Keywords

asymptotic normalityquadratic formlinear processintegrated periodogramsemiparametric and kernel estimation

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05)

Related Items (22)

Convergence of quadratic forms with nonvanishing diagonal ⋮ Two estimators of the long-run variance: beyond short memory ⋮ Central limit theorems for arrays of decimated linear processes ⋮ Weak convergence of linear and quadratic forms and related statements on \(L_p\)-approximability ⋮ Estimation of the memory parameter by fitting fractionally differenced autoregressive models ⋮ Nonlinear wavelet-based estimation to spectral density for stationary non-Gaussian linear processes ⋮ CONTEMPORANEOUS AGGREGATION OF TRIANGULAR ARRAY OF RANDOM-COEFFICIENT AR(1) PROCESSES ⋮ A note on quadratic forms of stationary functional time series under mild conditions ⋮ Asymptotic normality of quadratic forms of martingale differences ⋮ Tests for the Equality of Two Processes' Spectral Densities with Unequal Lengths Using Wavelet Methods ⋮ A martingale decomposition for quadratic forms of Markov chains (with applications) ⋮ On asymptotic distributions of weighted sums of periodograms ⋮ Inference of weighted \(V\)-statistics for nonstationary time series and its applications ⋮ Asymptotic normality of the mixture density estimator in a disaggregation scheme ⋮ Mean and autocovariance function estimation near the boundary of stationarity ⋮ Minimum distance lack-of-fit tests under long memory errors ⋮ Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields ⋮ The asymptotic behavior of quadratic forms in \(\varphi\)-mixing random variables ⋮ Central limit theorems for double Poisson integrals ⋮ LLN for quadratic forms of long memory time series and its applications in random matrix theory ⋮ Estimation pitfalls when the noise is not i.i.d. ⋮ A least squares method for variance estimation in heteroscedastic nonparametric regression

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