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ESTIMATION OF A SEMIPARAMETRIC IGARCH(1,1) MODEL

Published online by Cambridge University Press:  04 November 2010

Woocheol Kim  and
Oliver Linton
Woocheol Kim
Affiliation:
Korea Institute of Public Finance
Oliver Linton*
Affiliation:
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: [email protected].
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Abstract

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.

Type
ARTICLES
Information
Econometric Theory , Volume 27 , Issue 3: SPECIAL ISSUE ON INVERSE PROBLEMS IN ECONOMETRICS , June 2011 , pp. 639 - 661
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Blundell, R., Chen, X., & Kristensen, D. (2007) Semi-nonparametric IV estimation of shape-invariant Engle curves. Econometrica 75, 1613–1669.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. 5633–5751. 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, 289–314.Google Scholar
Engle, R.F. & Bollerslev, T. (1986) Modelling the persistence of conditional variances. Econometric Reviews 5, 1–50.Google Scholar
Hall, P. & Horowitz, J.L. (2005) Nonparametric methods for inference in the presence of instrumental variables. Annals of Statistics 33, 2904–2909.Google Scholar
Harvey, A., Ruiz, E., & Shephard, N. (1994) Multivariate stochastic variance models. Review of Economic Studies 61, 247–1264.Google Scholar
Hill, B.M. (1975) A simple general approach to inference about the tail of a distribution. Annals of Statistics 3, 1163–1174.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, 29–52.Google Scholar
Linton, O.B. & Mammen, E. (2005) Estimating semiparametric ARCH(∞) models by kernel smoothing methods. Econometrica 73, 771–836.Google Scholar
Masry, E. (1996) Multivariate local polynomial regression for time series: Uniform strong consistency and rates. Journal of Time Series Analysis 17, 571–599.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, 318–334.CrossRefGoogle Scholar
Newey, W.K. & Powell, J.L. (2003) Instrumental variable estimation of nonparametric models. Econometrica 71(5), 1565–1578.CrossRefGoogle Scholar
Rahbek, A. & Jensen, S.T. (2004) Asymptotic normality for nonstationary, explosive GARCH. Econometric Theory 20, 1203–1226.Google Scholar
Tautenhahn, U. (1998) Optimality for ill-posed problems under general source conditions. Numerical Functional Analyses and Optimizations 19, 377–398.Google Scholar