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Modelling Conditional and Unconditional Heteroskedasticity with Smoothly Time-Varying Structure

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  • Christina Amado
  • Timo Teräsvirta

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

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 ad- ditive 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 School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-08.

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Length: 56
Date of creation: 28 Jan 2008
Date of revision:
Handle: RePEc:aah:create:2008-08

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Web page: http://www.econ.au.dk/afn/

Related research

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.
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  3. Stefan Lundbergh & Timo Teräsvirta, 1999. "Evaluating GARCH Models," Tinbergen Institute Discussion Papers 99-008/4, Tinbergen Institute.
  4. 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.
  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. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
  8. 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.
  9. 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.
  10. Timo Terasvirta & Zhenfang Zhao, 2011. "Stylized facts of return series, robust estimates and three popular models of volatility," Applied Financial Economics, Taylor & Francis Journals, vol. 21(1-2), pages 67-94.
  11. 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.
  12. 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.
  13. 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.
  14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  15. Russell Davidson & James G. MacKinnon, 1994. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," Working Papers 903, Queen's University, Department of Economics.
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Citations

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Cited by:
  1. Fernando Alexandre & Miguel Portela & Carla Sá, 2008. "Admission conditions and graduates' employability," NIPE Working Papers 16/2008, NIPE - Universidade do Minho.
  2. 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.
  3. Francesco Battaglia & Mattheos Protopapas, 2009. "Time-varying Multi-regime Models Fitting by Genetic Algorithms," Working Papers 009, COMISEF.
  4. 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.
  5. 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.
  6. Paulo Bastos & Natália P. Monteiro, 2011. "Managers and Wage Policies," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 20(4), pages 957-984, December.
  7. 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.
  8. 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.
  9. 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).
  10. 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.
  11. 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.
  12. Rohan, Neelabh, 2013. "A time varying GARCH(p,q) model and related statistical inference," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 1983-1990.
  13. 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.
  14. 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.

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