MIXING PROPERTIES OF A GENERAL CLASS OF GARCH(1,1) MODELS WITHOUT MOMENT ASSUMPTIONS ON THE OBSERVED PROCESS
Econometric TheoryPublished 30 August 2006
Christian Francq, Jean‐Michel Zakoïan
Citations133
SJR quartileQ1
SJR score2.67
SNIP1.32
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
International audience
Keywords
MathematicsEconomics, Econometrics and Finance
Journal of EconometricsGeneralized autoregressive conditional heteroskedasticity
22,300 Citations1986Tim Bollerslev
EconometricaAutoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation
20,637 Citations1982Robert F. Engle
BiometrikaTesting for a unit root in time series regression
17,948 Citations1988Peter C.B. Phillips, Pierre Perrón
The Journal of FinanceOn the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks
8,683 Citations1993Lawrence R. Glosten, Ravi Jagannathan +1 more
Markov Chains and Stochastic Stability
5,130 Citations1993Sean Meyn, Richard L. Tweedie
This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.
TechnometricsTime Series: Theory and Methods
5,090 Citations1992Eric R. Ziegel, Peter J. Brockwell +1 more
The Journal of FinanceWhy Does Stock Market Volatility Change Over Time?
3,554 Citations1989G. William Schwert
Journal of Empirical FinanceA long memory property of stock market returns and a new model
3,262 Citations1993Zhuanxin Ding, Clive W. J. Granger +1 more
Journal of Economic Dynamics and ControlThreshold heteroskedastic models
2,264 Citations1994Jean‐Michel Zakoïan
The Journal of FinanceOn the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks
2,178 Citations1993Lawrence R. Glosten, Ravi Jagannathan +1 more
World Scientific Publishing Co. Pte. Ltd. eBooksModelling Financial Time Series
1,456 Citations2007Stephen J. Taylor
BiometrikaTesting for a Unit Root in Time Series Regression
1,420 Citations1988Peter C.B. Phillips, Pierre Perrón
Econometric TheoryStationarity and Persistence in the GARCH(1,1) Model
1,127 Citations1990Daniel B. Nelson
Theory of Probability and Its ApplicationsSome Limit Theorems for Stationary Processes
865 Citations1962И. А. Ибрагимов
Econometric TheoryAsymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator
637 Citations1994Sangwon Lee, Bruce E. Hansen
Econometric TheoryMIXING AND MOMENT PROPERTIES OF VARIOUS GARCH AND STOCHASTIC VOLATILITY MODELS
594 Citations2002Marine Carrasco, Xiaohong Chen
BernoulliMaximum likelihood estimation of pure GARCH and ARMA-GARCH processes
584 Citations2004Christian Francq, Jean‐Michel Zakoïan
Journal of EconometricsStationarity of Garch processes and of some nonnegative time series
580 Citations1992Philippe Bougerol, Nico Picard
EconometricaConsistency and Asymptotic Normality of the Quasi-Maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models
466 Citations1996Robin L. Lumsdaine
Birkhäuser Boston eBooksBasic Properties of Strong Mixing Conditions
436 Citations1986Richard C. Bradley
Stochastic Processes and their ApplicationsRegular variation of GARCH processes
382 Citations2002Bojan Basrak, Richard A. Davis +1 more
Journal of EconometricsAugmented GARCH (p,q) process and its diffusion limit
379 Citations1997Jin‐Chuan Duan
The strict stationarity of the augmented GARCH process is characterized and this process is shown to contain many existing parametric GARCH models that are commonly used for modeling stochastic volatility in the finance literature.
Journal of EconometricsStationarity and the existence of moments of a family of GARCH processes
360 Citations2002Shiqing Ling, Michael McAleer
The Annals of ProbabilityA Functional Central Limit Theorem for Weakly Dependent Sequences of Random Variables
291 Citations1984Norbert Herrndorf
Journal of EconometricsProperties of moments of a family of GARCH processes
278 Citations1999Changli He, Timo Teräsvirta
Theory of Probability and Its ApplicationsMixing Conditions for Markov Chains
262 Citations1974Yu. A. Davydov
Advances in Applied ProbabilityNon-linear time series and Markov chains
248 Citations1990Dag Tjøstheim
Journal of Applied ProbabilityA continuous-time GARCH process driven by a Lévy process: stationarity and second-order behaviour
243 Citations2004Claudia Klüppelberg, Alexander Lindner +1 more
Journal of Time Series AnalysisRANDOM COEFFICIENT AUTOREGRESSIVE PROCESSES:A MARKOV CHAIN ANALYSIS OF STATIONARITY AND FINITENESS OF MOMENTS
214 Citations1985Paul D. Feigin, Richard L. Tweedie
Journal of the American Statistical AssociationInference for Autocorrelations under Weak Assumptions
189 Citations1996Joseph P. Romano, Lori A. Thombs
EconometricaAsymptotic Normality of the QMLE Estimator of ARCH in the Nonstationary Case
151 Citations2004Søren Jensen, Anders Rahbek
The Journal of FinanceHeteroskedasticity in Stock Returns
141 Citations1990G. William Schwert, Paul J. Seguin
Econometric TheoryERGODICITY, MIXING, AND EXISTENCE OF MOMENTS OF A CLASS OF MARKOV MODELS WITH APPLICATIONS TO GARCH AND ACD MODELS
140 Citations2008Mika Meitz, Pentti Saikkonen
Journal of Applied EconometricsSIGN- AND VOLATILITY-SWITCHING ARCH MODELS: THEORY AND APPLICATIONS TO INTERNATIONAL STOCK MARKETS
135 Citations1997Fabio Fornari, Antonio Mele
Stochastic Processes and their ApplicationsThe mixing property of bilinear and generalised random coefficient autoregressive models
121 Citations1986Pham Dinh Tuan
Journal of Statistical Planning and InferenceEstimating linear representations of nonlinear processes
98 Citations1998Christian Francq, Jean‐Michel Zakoïan
Econometric ReviewsEstimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence
74 Citations2003Shiqing Ling, W. K. Li +1 more
Journal of the American Statistical AssociationInference For Autocorrelations Under Weak Assumptions
39 Citations1996Joseph P. Romano, Lori A. Thombs
Stochastic Processes and their ApplicationsPower transformation and threshold modeling for ARCH innovations with applications to tests for ARCH structure
38 Citations2003Sun Young Hwang, Tae Yoon Kim
Statistics & Probability LettersA note on geometric ergodicity of autoregressive conditional heteroscedasticity (ARCH) model
26 Citations1996Zudi Lu
For the pth-order linear ARCH model, , where [alpha]0 > 0, [ alpha]i [greater-or-equal, slanted] 0, I = 1, 2, ..., p, {[var epsilon]t} is an i.i.d. normal white noise with E[var Epsilon].
Economics LettersMoving average conditional heteroskedastic processes
15 Citations1995Minxian Yang, Ronald Bewley
Comptes Rendus de l Académie des Sciences - Series I - MathematicsCritères d'ergodicité géométrique ou arithmétique de modèles linéaires pertubés à représentation markovienne
12 Citations1998Patrick Ango Nze
Repository for Publications and Research Data (ETH Zurich)Nonparametric GARCH models
8 Citations1999Peter Bühlmann, Alexander J. McNeil
It is observed that the nonparametric procedure often gives better estimates of the unobserved latent volatility process than parametric GARCH(1,1) modelling, particularly when asymmetries are present in the data.
Economics LettersStrict stationarity and mixing properties of asymmetric power GARCH models allowing a signed volatility
6 Citations2004O. Lee, Dong Wan Shin