Hostname: page-component-797576ffbb-vjhkx Total loading time: 0 Render date: 2023-12-08T12:00:23.301Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": true, "coreDisableEcommerce": false, "useRatesEcommerce": true } hasContentIssue false


Published online by Cambridge University Press:  04 November 2010

Woocheol Kim
Korea Institute of Public Finance
Oliver Linton*
London School of Economics
*Address correspondence to Oliver Linton, Department of Economics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom; e-mail:


We propose a semiparametric IGARCH model that allows for persistence in variance but also allows for more flexible functional form. We assume that the difference of the squared process is weakly stationary. We propose an estimation strategy based on the nonparametric instrumental variable method. We establish the rate of convergence of our estimator.

Copyright © Cambridge University Press 2011

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.)



Blundell, R., Chen, X., & Kristensen, D. (2007) Semi-nonparametric IV estimation of shape-invariant Engle curves. Econometrica 75, 16131669.Google Scholar
Carrasco, M., Florens, J.P., & Renault, E. (2006) Linear inverse problems in structural econometrics. In Heckman, J.J. & Leamer, E. (eds.), Handbook of Econometrics, vol. 6, pp. 56335751. Elsevier.Google Scholar
Chen, X. & Reiss, M. (2010) On rate optimality for ill-posed inverse problems in econometrics. Econometric Theory 27 (this issue).Google Scholar
Chen, X. & Shen, X. (1998) Sieve extremum estimates for weakly dependent data. Econometrica 66, 289314.Google Scholar
Engle, R.F. & Bollerslev, T. (1986) Modelling the persistence of conditional variances. Econometric Reviews 5, 150.Google Scholar
Hall, P. & Horowitz, J.L. (2005) Nonparametric methods for inference in the presence of instrumental variables. Annals of Statistics 33, 29042909.Google Scholar
Harvey, A., Ruiz, E., & Shephard, N. (1994) Multivariate stochastic variance models. Review of Economic Studies 61, 2471264.Google Scholar
Hill, B.M. (1975) A simple general approach to inference about the tail of a distribution. Annals of Statistics 3, 11631174.Google Scholar
Kim, W. (2003) Identification and Estimation of Nonparametric Structural Models by Instrumental Variables Method. Manuscript, Humboldt University.Google Scholar
Lee, S. & Hansen, B. (1994) Asymptotic theory for the GARCH(1,1) quasi-maximum likelihood estimator. Econometric Theory 10, 2952.Google Scholar
Linton, O.B. & Mammen, E. (2005) Estimating semiparametric ARCH(∞) models by kernel smoothing methods. Econometrica 73, 771836.Google Scholar
Masry, E. (1996) Multivariate local polynomial regression for time series: Uniform strong consistency and rates. Journal of Time Series Analysis 17, 571599.Google Scholar
Meitz, M. & Saikkonen, P. (2004) Ergodicity, Mixing, and Existence of Moments for a Class of Markov Models with Applications to GARCH and ACD Models. Manuscript, Stockholm School of Economics.Google Scholar
Nelson, D. (1990) Stationarity and persistence in the GARCH(1,1) models. Econometric Theory 6, 318334.Google Scholar
Newey, W.K. & Powell, J.L. (2003) Instrumental variable estimation of nonparametric models. Econometrica 71(5), 15651578.Google Scholar
Rahbek, A. & Jensen, S.T. (2004) Asymptotic normality for nonstationary, explosive GARCH. Econometric Theory 20, 12031226.Google Scholar
Tautenhahn, U. (1998) Optimality for ill-posed problems under general source conditions. Numerical Functional Analyses and Optimizations 19, 377398.Google Scholar