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Let's get LADE: robust estimation of semiparametric multiplicative volatility models

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  • Bonsoo Koo
  • Oliver Linton

Abstract

We investigate a model in which we connect slowly time varying unconditional long-run volatility with short-run conditional volatility whose representation is given as a semi-strong GARCH (1,1) process with heavy tailed errors. We focus on robust estimation of both long-run and short-run volatilities. Our estimation is semiparamentric since the long-run volatility is totally unspecified whereas the short-run conditional volatility is a parametric semi-strong GARCH (1,1) process. We propose different robust estimation methods for nonstationary and strictly stationary GARCH parameters with non-parametric long-run volatility function. Our estimation is based on a two-step LAD procedure. We establish the relevant asymptotic theory of the proposed estimators. Numerical results lend support to our theoretical results.

Suggested Citation

  • Bonsoo Koo & Oliver Linton, 2013. "Let's get LADE: robust estimation of semiparametric multiplicative volatility models," CeMMAP working papers 11/13, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:11/13
    DOI: 10.1920/wp.cem.2013.1113
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    1. Linton, Oliver & Pan, Jiazhu & Wang, Hui, 2010. "Estimation For A Nonstationary Semi-Strong Garch(1,1) Model With Heavy-Tailed Errors," Econometric Theory, Cambridge University Press, vol. 26(1), pages 1-28, February.
    2. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    3. Søren Tolver Jensen & Anders Rahbek, 2004. "Asymptotic Normality of the QMLE Estimator of ARCH in the Nonstationary Case," Econometrica, Econometric Society, vol. 72(2), pages 641-646, March.
    4. Ai, Chunrong & Chen, Xiaohong, 2012. "The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions," Journal of Econometrics, Elsevier, vol. 170(2), pages 442-457.
    5. Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," The Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
    6. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    7. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    8. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2010. "Uniform Bahadur Representation For Local Polynomial Estimates Of M-Regression And Its Application To The Additive Model," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1529-1564, October.
    9. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    10. VAN BELLEGEM, Sébastien, 2011. "Locally stationary volatility modelling," LIDAM Discussion Papers CORE 2011041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Biometrika Trust, vol. 90(4), pages 967-975, December.
    12. Peng, Liang & Yao, Qiwei, 2003. "Least absolute deviations estimation for ARCH and GARCH models," LSE Research Online Documents on Economics 5828, London School of Economics and Political Science, LSE Library.
    13. Hall, Peter & Peng, Liang & Yao, Qiwei, 2002. "Prediction and nonparametric estimation for time series with heavy tails," LSE Research Online Documents on Economics 6086, London School of Economics and Political Science, LSE Library.
    14. Juan Rodríguez-Poo & Oliver Linton, 2001. "Nonparametric factor analysis of residual time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 161-182, June.
    15. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
    16. Delgado, Miguel A. & Hidalgo, Javier, 2000. "Nonparametric inference on structural breaks," Journal of Econometrics, Elsevier, vol. 96(1), pages 113-144, May.
    17. Wolfgang Härdle & Pham‐Dinh Tuan, 1986. "Some Theory On M‐Smoothing Of Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(3), pages 191-204, May.
    18. Peter Hall & Liang Peng & Qiwei Yao, 2002. "Prediction and nonparametric estimation for time series with heavy tails," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(3), pages 313-331, May.
    19. Bikbov, Ruslan & Chernov, Mikhail, 2010. "No-arbitrage macroeconomic determinants of the yield curve," Journal of Econometrics, Elsevier, vol. 159(1), pages 166-182, November.
    20. Veronesi, Pietro, 1999. "Stock Market Overreaction to Bad News in Good Times: A Rational Expectations Equilibrium Model," The Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 975-1007.
    21. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    22. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(1), pages 29-52, March.
    23. Koo, Bonsoo & Linton, Oliver, 2012. "Estimation of semiparametric locally stationary diffusion models," Journal of Econometrics, Elsevier, vol. 170(1), pages 210-233.
    24. repec:hal:journl:peer-00732517 is not listed on IDEAS
    25. Francq, Christian & Zakoïan, Jean-Michel, 2006. "Mixing Properties Of A General Class Of Garch(1,1) Models Without Moment Assumptions On The Observed Process," Econometric Theory, Cambridge University Press, vol. 22(5), pages 815-834, October.
    26. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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