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Simultaneously Modeling Conditional Heteroskedasticity And Scale Change

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  • Feng, Yuanhua

Abstract

This paper proposes a semiparametric approach by introducing a smooth scale function into the standard generalized autoregressive conditional heteroskedastic (GARCH) model so that conditional heteroskedasticity (CH) and scale change in financial returns can be modeled simultaneously. An estimation procedure combining kernel estimation of the scale function and maximum likelihood estimation of the GARCH parameters is proposed. Asymptotic properties of the estimators are investigated in detail. It is shown that asymptotically normal, -consistent parameter estimation is available. A data-driven algorithm is developed for practical implementation. Finite sample performance of the proposal is studied through simulation. The proposal is applied to model CH and scale change in the daily S P 500 and DAX 100 returns. It is shown that both series have simultaneously significant scale change and CH.We are very grateful to the co-editor and two referees for their helpful comments and suggestions, which led to a substantial improvement of this paper. The paper was finished under the advice of Professor Jan Beran, Department of Mathematics and Statistics, University of Konstanz, Germany, and was financially supported by the Center of Finance and Econometrics (CoFE), University of Konstanz. We thank colleagues in CoFE, especially Professor Winfried Pohlmeier, for their interesting questions at a talk of the author. It was these questions that motivated the author to write this paper. Our special thanks go to Dr. Erik L ders, Department of Finance and Insurance, Laval University, and Stern School of Business, New York University, for his helpful suggestions.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 20 (2004)
Issue (Month): 03 (June)
Pages: 563-596

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Handle: RePEc:cup:etheor:v:20:y:2004:i:03:p:563-596_20

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References

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  1. He, Changli & Ter svirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(06), pages 824-846, December.
  2. Jan Beran & Yuanhua Feng, 2002. "Local Polynomial Fitting with Long-Memory, Short-Memory and Antipersistent Errors," Annals of the Institute of Statistical Mathematics, Springer, vol. 54(2), pages 291-311, June.
  3. Beran, Jan & Feng, Yuanhua, 2002. "SEMIFAR models--a semiparametric approach to modelling trends, long-range dependence and nonstationarity," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 393-419, August.
  4. Jan Beran, 1999. "SEMIFAR Models - A Semiparametric Framework for Modelling Trends, Long Range Dependence and Nonstationarity," CoFE Discussion Paper 99-16, Center of Finance and Econometrics, University of Konstanz.
  5. Karanasos, Menelaos, 1999. "The second moment and the autocovariance function of the squared errors of the GARCH model," Journal of Econometrics, Elsevier, vol. 90(1), pages 63-76, May.
  6. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  7. Jan Beran & Yuanhua.Feng, 2001. "Iterative plug-in algorithms for SEMIFAR models - definition, convergence and asymptotic properties," CoFE Discussion Paper 01-11, Center of Finance and Econometrics, University of Konstanz.
  8. Shiqing Ling & Michael McAleer, 2001. "Necessary and Sufficient Moment Conditions for the GARCH(r,s) and Asymmetric Power GARCH(r,s) Models," ISER Discussion Paper 0534, Institute of Social and Economic Research, Osaka University.
  9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  10. Jan Beran & Yuanhua Feng, 1999. "Local Polynomial Estimation with a FARIMA-GARCH Error Process," CoFE Discussion Paper 99-08, Center of Finance and Econometrics, University of Konstanz.
  11. Beran, Jan & Ocker, Dirk, 2001. "Volatility of Stock-Market Indexes--An Analysis Based on SEMIFAR Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 103-16, January.
  12. Hall, Peter & Hart, Jeffrey D., 1990. "Nonparametric regression with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 36(2), pages 339-351, December.
  13. Wolfgang HÄRDLE & A. TSYBAKOV & L. YANG, 1996. "Nonparametric Vector Autoregression," SFB 373 Discussion Papers 1996,61, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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Citations

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Cited by:
  1. Feng, Yuanhua & McNeil, Alexander J., 2008. "Modelling of scale change, periodicity and conditional heteroskedasticity in return volatility," Economic Modelling, Elsevier, vol. 25(5), pages 850-867, September.
  2. Feng, Yuanhua, 2006. "A local dynamic conditional correlation model," MPRA Paper 1592, University Library of Munich, Germany.
  3. Amado, Cristina & Teräsvirta, Timo, 2014. "Modelling changes in the unconditional variance of long stock return series," Journal of Empirical Finance, Elsevier, vol. 25(C), pages 15-35.
  4. Jan Beran & Yuanhua.Feng, 2002. "Recent Developments in Non- and Semiparametric Regression with Fractional Time Series Errors," CoFE Discussion Paper 02-13, Center of Finance and Econometrics, University of Konstanz.
  5. Yuanhua Feng, 2002. "Modelling Different Volatility Components in High-Frequency Financial Returns," CoFE Discussion Paper 02-18, Center of Finance and Econometrics, University of Konstanz.
  6. Feng, Yuanhua & Yu, Keming, 2006. "Nonparametric estimation of time-varying covariance matrix in a slowly changing vector random walk model," MPRA Paper 1597, University Library of Munich, Germany.
  7. Yuanhua Feng, 2013. "Double-conditional smoothing of high-frequency volatility surface in a spatial multiplicative component GARCH with random effects," Working Papers CIE 65, University of Paderborn, CIE Center for International Economics.
  8. repec:pdn:wpaper:65 is not listed on IDEAS
  9. Jing Wang, 2012. "Modelling time trend via spline confidence band," Annals of the Institute of Statistical Mathematics, Springer, vol. 64(2), pages 275-301, April.
  10. repec:pdn:wpaper:66 is not listed on IDEAS

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