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Modelling Conditional and Unconditional Heteroskedasticity with Smoothly Time-Varying Structure

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  • Amado, Cristina

    ()
    (University of Minho and NIPE)

  • Teräsvirta, Timo

    ()
    (CREATES, University of Aarhus)

Abstract

In this paper, we propose two parametric alternatives to the standard GARCH model. They allow the conditional variance to have a smooth time-varying structure of either additive or multiplicative type. The suggested parameterizations describe both nonlinearity and structural change in the conditional and unconditional variances where the transition between regimes over time is smooth. A modelling strategy for these new time-varying parameter GARCH models is developed. It relies on a sequence of Lagrange multiplier tests, and the adequacy of the estimated models is investigated by Lagrange multiplier type misspecification tests. Finite-sample properties of these procedures and tests are examined by simulation. An empirical application to daily stock returns and another one to daily exchange rate returns illustrate the functioning and properties of our modelling strategy in practice. The results show that the long memory type behaviour of the sample autocorrelation functions of the absolute returns can also be explained by deterministic changes in the unconditional variance.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 691.

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Length: 56 pages
Date of creation: 24 Jan 2008
Date of revision:
Publication status: Published as Amado, Cristina and Timo Teräsvirta, 'Modelling volatility by variance decomposition' in Journal of Econometrics, 2013, pages 142-153.
Handle: RePEc:hhs:hastef:0691

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Keywords: Conditional heteroskedasticity; Structural change; Lagrange multiplier test; Misspecification test; Nonlinear time series; Time-varying parameter model.;

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References

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  1. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, vol. 62(2), pages 211-228, June.
  2. Jensen, S ren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1203-1226, December.
  3. Robert F. Engle & Jose Gonzalo Rangel, 2005. "The Spline GARCH Model for Unconditional Volatility and its Global Macroeconomic Causes," Working Papers 2005/13, Czech National Bank, Research Department.
  4. Kim, Tae-Hwan & White, Halbert, 2004. "On more robust estimation of skewness and kurtosis," Finance Research Letters, Elsevier, vol. 1(1), pages 56-73, March.
  5. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
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  7. Mika Meitz & Pentti Saikkonen, 2007. "Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models," Economics Series Working Papers 327, University of Oxford, Department of Economics.
  8. Berkes, Istv n & Gombay, Edit & Horv th, Lajos & Kokoszka, Piotr, 2004. "SEQUENTIAL CHANGE-POINT DETECTION IN GARCH(p,q) MODELS," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1140-1167, December.
  9. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper 0549, Institute of Social and Economic Research, Osaka University.
  10. Richard T. Baillie & Claudio Morana, 2007. "Modeling Long Memory and Structural Breaks in Conditional Variances: an Adaptive FIGARCH Approach," ICER Working Papers - Applied Mathematics Series 11-2007, ICER - International Centre for Economic Research.
  11. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  12. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
  13. Teräsvirta, Timo & Zhao, Zhenfang, 2007. "Stylized Facts of Return Series, Robust Estimates, and Three Popular Models of Volatility," Working Paper Series in Economics and Finance 662, Stockholm School of Economics, revised 05 Jun 2007.
  14. Eitrheim, Øyvind & Teräsvirta, Timo, 1995. "Testing the Adequacy of Smooth Transition Autoregressive Models," Working Paper Series in Economics and Finance 56, Stockholm School of Economics.
  15. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 225-34, April.
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Citations

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Cited by:
  1. Claudio Morana, 2014. "Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks," Working Papers 273, University of Milano-Bicocca, Department of Economics, revised May 2014.
  2. Natália P. Monteiro & Paulo Bastos, 2009. "Managers and wage policies," NIPE Working Papers 2/2009, NIPE - Universidade do Minho.
  3. Francesco Battaglia & Mattheos Protopapas, 2009. "Time-varying Multi-regime Models Fitting by Genetic Algorithms," Working Papers 009, COMISEF.
  4. Chen, Cathy W.S. & Gerlach, Richard & Lin, Edward M.H., 2014. "Bayesian estimation of smoothly mixing time-varying parameter GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 194-209.
  5. Claudio Morana, 2010. "Heteroskedastic Factor Vector Autoregressive Estimation of Persistent and Non Persistent Processes Subject to Structural Breaks," ICER Working Papers - Applied Mathematics Series 36-2010, ICER - International Centre for Economic Research.
  6. Frijns, Bart & Lehnert, Thorsten & Zwinkels, Remco C.J., 2011. "Modeling structural changes in the volatility process," Journal of Empirical Finance, Elsevier, vol. 18(3), pages 522-532, June.
  7. Rohan, Neelabh, 2013. "A time varying GARCH(p,q) model and related statistical inference," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 1983-1990.
  8. Fernando Alexandre & Miguel Portela & Carla Sá, 2008. "Admission conditions and graduates' employability," NIPE Working Papers 16/2008, NIPE - Universidade do Minho.
  9. Adnen Ben Nasr & Mohamed Boutahar & Abdelwahed Trabelsi, 2010. "Fractionally integrated time varying GARCH model," Statistical Methods and Applications, Springer, vol. 19(3), pages 399-430, August.
  10. Adnen Ben Nasr & Ahdi N. Ajmi & Rangan Gupta, 2013. "Modeling the Volatility of the Dow Jones Islamic Market World Index Using a Fractionally Integrated Time Varying GARCH (FITVGARCH) Model," Working Papers 201357, University of Pretoria, Department of Economics.
  11. Claudio Morana, 2013. "Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks: New Insights on the US OIS SPreads Term Structure," Working Papers 233, University of Milano-Bicocca, Department of Economics, revised Feb 2013.
  12. BAUWENS, Luc & DUFAYS, Arnaud & DE BACKER, Bruno, 2011. "Estimating and forecasting structural breaks in financial time series," CORE Discussion Papers 2011055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. Matteo Barigozzi & Christian T. Brownlees & Giampiero M. Gallo & David Veredas, 2014. "Disentangling Systematic and Idiosyncratic Dynamics in Panels of Volatility Measures," Econometrics Working Papers Archive 2014_02, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", revised Feb 2014.
  14. Błażej Mazur & Mateusz Pipień, 2012. "On the Empirical Importance of Periodicity in the Volatility of Financial Returns - Time Varying GARCH as a Second Order APC(2) Process," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 4(2), pages 95-116, June.

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