ON STATIONARITY IN THE ARCH(∞) MODEL

Vytautas Kazakevičius; Remigijus Leipus

doi:10.1017/S0266466602181011

Abstract

We continue investigation of the ARCH(∞) model begun in Giraitis, Kokoszka, and Leipus (2000, Econometric Theory 16, 3–22). Nonrestrictive conditions for the existence of a strictly stationary solution are established. The paper generalizes the results of Nelson (1990, Econometric Theory 6, 318–334) and Bougerol and Picard (1992, Journal of Econometrics 52, 115–127) to the ARCH(∞) model.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Koulikov, Dmitri 2002. Modeling Sequences of Long Memory Non-negative Covariance Stationary Random Variables. SSRN Electronic Journal ,

Kazakevičius, Vytautas and Leipus, Remigijus 2003. A new theorem on the existence of invariant distributions with applications to ARCH processes. Journal of Applied Probability, Vol. 40, Issue. 1, p. 147.

Berkes, István and Horváth, Lajos 2003. Limit results for the empirical process of squared residuals in GARCH models. Stochastic Processes and their Applications, Vol. 105, Issue. 2, p. 271.

Teyssière, Gilles 2003. Processes with Long-Range Correlations. Vol. 621, Issue. , p. 251.

Davidson, James 2004. Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model. Journal of Business & Economic Statistics, Vol. 22, Issue. 1, p. 16.

Kazakevičius, Vytautas Leipus, Remigijus and Viano, Marie-Claude 2004. Stability of random coefficient ARCH models and aggregation schemes. Journal of Econometrics, Vol. 120, Issue. 1, p. 139.

Kirman, Alan and Teyssière, Gilles 2005. Testing for bubbles and change-points. Journal of Economic Dynamics and Control, Vol. 29, Issue. 4, p. 765.

Robinson, Peter M. and Zaffaroni, Paolo 2006. Pseudo-maximum likelihood estimation of ARCH(∞) models. The Annals of Statistics, Vol. 34, Issue. 3,

Doukhan, Paul Madre, Hélène and Rosenbaum, Mathieu 2007. Weak dependence for infinite ARCH-type bilinear models. Statistics, Vol. 41, Issue. 1, p. 31.

Bordignon, Silvano Caporin, Massimiliano and Lisi, Francesco 2007. Generalised long-memory GARCH models for intra-daily volatility. Computational Statistics & Data Analysis, Vol. 51, Issue. 12, p. 5900.

Francq, Christian and Zakoian, Jean-Michel 2007. Quasi-maximum likelihood estimation in GARCH processes when some coefficients are equal to zero. Stochastic Processes and their Applications, Vol. 117, Issue. 9, p. 1265.

Giraitis, Liudas Leipus, Remigijus and Surgailis, Donatas 2007. Long Memory in Economics. p. 3.

Lee, O. and Kim, H.M. 2008. Covariance stationary GARCH-family models with long memory property. Journal of the Korean Statistical Society, Vol. 37, Issue. 1, p. 29.

Lahiani, Amine and Yousfi, Ouidad 2008. Long Memory GARCH Processes: Empirical Evidence from the Tunisian Stock Exchange Market. SSRN Electronic Journal,

Baillie, Richard T. and Morana, Claudio 2009. Modelling long memory and structural breaks in conditional variances: An adaptive FIGARCH approach. Journal of Economic Dynamics and Control, Vol. 33, Issue. 8, p. 1577.

Giraitis, Liudas Leipus, Remigijus and Surgailis, Donatas 2009. Handbook of Financial Time Series. p. 71.

Kristensen, Dennis 2009. On stationarity and ergodicity of the bilinear model with applications to GARCH models. Journal of Time Series Analysis, Vol. 30, Issue. 1, p. 125.

Paparoditis, Efstathios and Politis, Dimitris N. 2009. Handbook of Financial Time Series. p. 983.

Davies, Antony 2009. Human development and the optimal size of government. The Journal of Socio-Economics, Vol. 38, Issue. 2, p. 326.

Download full list

Article contents

ON STATIONARITY IN THE ARCH(∞) MODEL

Abstract

Access options

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

ON STATIONARITY IN THE ARCH(∞) MODEL

Abstract

Access options

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests