Hostname: page-component-7dd5485656-jtdwj Total loading time: 0 Render date: 2025-10-30T08:51:29.791Z Has data issue: false hasContentIssue false
  • English
  • Français

ARCHIMEDEAN COPULAS AND TEMPORAL DEPENDENCE

Published online by Cambridge University Press:  27 April 2012

Brendan K. Beare
Brendan K. Beare*
Affiliation:
University of California, San Diego
*
*Address correspondence to Brendan Beare, Department of Economics, University of California-San Diego, 9500 Gilman Drive #0508, La Jolla, CA 92093-0508, USA; e-mail: bbeare@ucsd.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the dependence properties of stationary Markov chains generated by Archimedean copulas. Under some simple regularity conditions, we show that regular variation of the Archimedean generator at zero and one implies geometric ergodicity of the associated Markov chain. We verify our assumptions for a range of Archimedean copulas used in applications.

Information

Type
Articles
Information
Econometric Theory , Volume 28 , Issue 6 , December 2012 , pp. 1165 - 1185
Copyright
Copyright © Cambridge University Press 2012 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Andrews, D.W.K. (1984) Non strong mixing autoregressive processes. Journal of Applied Probability 21, 930–934.Google Scholar
Beare, B.K. (2010) Copulas and temporal dependence. Econometrica 78, 395–410.Google Scholar
Bingham, N.H., Goldie, C.M., & Teugels, J.L. (1987) Regular Variation. Cambridge University Press.Google Scholar
Bollerslev, T. (1986) Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307–327.CrossRefGoogle Scholar
Bouyé, E. & Salmon, M. (2009) Dynamic copula quantile regressions and tail area dynamic dependence in Forex markets. European Journal of Finance 15, 721–750.CrossRefGoogle Scholar
Box, G.E.P. & Jenkins, G.M. (1970) Time Series Analysis: Forecasting and Control. Holden-Day.Google Scholar
Bradley, R.C. (2007) Introduction to Strong Mixing Conditions, vols. 1 and 2. Kendrick Press.Google Scholar
Carrasco, M. & Chen, X. (2002) Mixing and moment properties of various GARCH and stochastic volatility models. Econometric Theory 18, 17–39.CrossRefGoogle Scholar
Charpentier, A. & Segers, J. (2007) Lower tail dependence for Archimedean copulas: Characterizations and pitfalls. Insurance: Mathematics and Economics 40, 525–532.Google Scholar
Chen, X. & Fan, Y. (2006) Estimation of copula-based semiparametric time series models. Journal of Econometrics 130, 307–335.CrossRefGoogle Scholar
Chen, X., Hansen, L.P., & Carrasco, M. (2010) Nonlinearity and temporal dependence. Journal of Econometrics 155, 155–169.CrossRefGoogle Scholar
Chen, X., Koenker, R., & Xiao, Z. (2009) Copula-based nonlinear quantile autoregression. Econometrics Journal 12, S50–S67.CrossRefGoogle Scholar
Chen, X., Wu, W.B., & Yi, Y. (2009) Efficient estimation of copula-based semiparametric Markov models. Annals of Statistics 37, 4214–4253.CrossRefGoogle Scholar
Darsow, W.F., Nguyen, B., & Olsen, E.T. (1992) Copulas and Markov processes. Illinois Journal of Mathematics 36, 600–642.Google Scholar
Davydov, Y.A. (1973) Mixing conditions for Markov chains. Theory of Probability and its Applications 18, 312–328.CrossRefGoogle Scholar
Engle, R.F. (1982) Autoregressive conditional heteroskedasticty with estimates of the variance of U.K. inflation. Econometrica 50, 987–1008.CrossRefGoogle Scholar
Engle, R.F. & Russell, J. (1998) Autoregressive conditional duration: A new model for irregularly spaced transaction data. Econometrica 66, 1127–1162.CrossRefGoogle Scholar
Fentaw, A. & Naik-Nimbalkar, U.V. (2008) Dynamic copula-based Markov time series. Communications in Statistics: Theory and Methods 37, 2447–2460.Google Scholar
Gagliardini, P. & Gouriéroux, C. (2008) Duration time-series models with proportional hazard. Journal of Time Series Analysis 29, 74–124.Google Scholar
Genest, C. & MacKay, J. (1986a) Copules archimédiennes et familles de lois bidimensionnelles dont les marges sont données. Canadian Journal of Statistics 14, 145–159.CrossRefGoogle Scholar
Genest, C. & MacKay, J. (1986b) The joy of copulas: Bivariate distributions with uniform marginals. American Statistician 40, 280–283.Google Scholar
Ibragimov, R. (2009) Copula-based characterizations for higher-order Markov processes. Econometric Theory 25, 819–846.CrossRefGoogle Scholar
Ibragimov, R. & Lentzas, G. (2009) Copulas and Long Memory. Harvard Institute of Economic Research Discussion Paper No. 2160.Google Scholar
Juri, A. & Wüthrich, M.V. (2002) Copula convergence theorems for tail events. Insurance: Mathematics and Economics 30, 411–427.Google Scholar
Juri, A. & Wüthrich, M.V. (2003) Tail dependence from a distributional point of view. Extremes 6, 213–246.CrossRefGoogle Scholar
Meitz, M. & Saikkonen, P. (2008) Ergodicity, mixing and existence of moments of a class of Markov models with applications to GARCH and ACD models. Econometric Theory 24, 1291–1320.CrossRefGoogle Scholar
Meyn, S.P. & Tweedie, R.L. (1993) Markov Chains and Stochastic Stability. Springer-Verlag.CrossRefGoogle Scholar
Mokkadem, A. (1988) Mixing properties of ARMA processes. Stochastic Processes and their Applications 29, 309–315.CrossRefGoogle Scholar
Nelsen, R.B. (2006) An Introduction to Copulas, 2nd ed. Springer-Verlag.Google Scholar
Pham, T.D. & Tran, L.T. (1985) Some mixing properties of time series models. Stochastic Processes and their Applications 19, 297–303.Google Scholar
Phillips, P.C.B. (2007) Regression with slowly varying regressors and nonlinear trends. Econometric Theory 23, 557–614.CrossRefGoogle Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.CrossRefGoogle Scholar