ARCH-type bilinear models with double long memory.
type: Item
instance of: scholarly article
title: ARCH-type bilinear models with double long memory.
zbMATH Open document ID: 1057.62070
DOI: 10.1016/S0304-4149(02)00108-4
author: L. Giraitis
author: Donatas Surgailis
published in: Stochastic Processes and their Applications
publication date: 2005-02-25T00:00:00Z
review text: The authors discuss the covariance structure and long-memory properties of stationary solutions of the bilinear equation \(X_t=\xi _tA_t +B_t\), where \(\xi _t,t\in Z\) are standard i.i.d.\ random variables and \(A_t,B_t\) are moving averages in \(X_t,\;s<t\). A stationary solution of the equation is obtained as a Volterra expansion. A number of particular cases is discussed.
reviewed by: Marie Hušková
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 2138928
zbMATH Keywords: ARCH processes
zbMATH Keywords: bilinear models
zbMATH Keywords: long memory
zbMATH Keywords: Volterra series
zbMATH Keywords: functional limit theorems
MaRDI profile type: Publication
cites work: Q5560061
cites work: Modeling and pricing long memory in stock market volatility
cites work: Stationarity of GARCH processes and of some nonnegative time series
cites work: Q4343010
cites work: Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation
cites work: STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM
cites work: A model for long memory conditional heteroscedasticity.
cites work: Q4158357
cites work: FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS
cites work: On stationary solutions of a stochastic differential equation
cites work: The second moment and the autocovariance function of the squared errors of the GARCH model
cites work: On Fractionally Integrated Autoregressive Moving-Average Time Series Models With Conditional Heteroscedasticity
cites work: Periodic solutions of affine stochastic differential equations
cites work: Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression
cites work: The memory of stochastic volatility models
cites work: Q4340161
cites work: Q4084474
cites work: An introduction to bispectral analysis and bilinear time series models
cites work: Zones of attraction of self-similar multiple integrals
cites work: Convergence of Appell polynomials of long range dependent moving averages in martingale differences
cites work: Weak convergence to fractional brownian motion and to the rosenblatt process
cites work: Bilinear stochastic models and related problems of nonlinear time series analysis. A frequency domain approach
cites work: A NOTE ON A MARKOV BILINEAR STOCHASTIC PROCESS IN DISCRETE TIME
Recommended article: ARCH(∞) Models and Long Memory Properties
Recommended article: Q3795104
Recommended article: STATIONARITY AND MEMORY OF ARCH([infty infinity]) MODELS
Recommended article: A Class of Nonlinear Arch Models
Recommended article: Stationary solution and parametric estimation for bilinear model driven by ARCH noises
Recommended article: Varieties of long memory models
Recommended article: Nonlinear autoregressive models and long memory
description: scientific article; zbMATH DE number 2138928