The functional central limit theorem for a family of GARCH observations with applications

DOI10.1016/j.spl.2008.03.021zbMath1151.60323OpenAlexW2170454421MaRDI QIDQ952866

Lajos Horváth, István Berkes, Siegfried Hörmann

Publication date: 14 November 2008

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2008.03.021

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Functional limit theorems; invariance principles (60F17)

Related Items

Asymptotics for semi-strong augmented GARCH(1,1) model, On weak invariance principles for partial sums, Functional central limit theorems for augmented GARCH(\(p\),\(q\)) and FIGARCH processes, Edgeworth expansions for volatility models, The functional central limit theorem for ARMA-GARCH processes, UNIT ROOT TESTS WITH WAVELETS, Stationarity and functional central limit theorem for ARCH(\(\infty\)) models, Berry-Esseen theorems under weak dependence, Extensions of some classical methods in change point analysis, Asymptotic results for the empirical process of stationary sequences, Optimal Rate of Convergence for Empirical Quantiles and Distribution Functions for Time Series, Break detection in the covariance structure of multivariate time series models, Structural breaks in time series, The functional central limit theorem for the multivariate MS-ARMA-GARCH model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Testing the null hypothesis of stationarity against the alternative of a unit root. How sure are we that economic time series have a unit root?
• Information regularity and the central limit question
• An invariance principle for certain dependent sequences
• GARCH (1,1) processes are near epoch dependent
• Stationarity of GARCH processes and of some nonnegative time series
• Strict stationarity of generalized autoregressive processes
• Augmented GARCH\((p,q)\) process and its diffusion limit
• A new weak dependence condition and applications to moment inequalities
• Generalized autoregressive conditional heteroscedasticity
• Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes.
• Rescaled variance and related tests for long memory in volatility and levels
• Detection of change in persistence of a linear time series
• Weak dependence. With examples and applications.
• Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation
• Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence
• MIXING AND MOMENT PROPERTIES OF VARIOUS GARCH AND STOCHASTIC VOLATILITY MODELS
• NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS
• STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM
• WEAK DEPENDENCE: MODELS AND APPLICATIONS TO ECONOMETRICS
• Some Limit Theorems for Stationary Processes