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Locally stationary volatility modelling

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  • VAN BELLEGEM, Sébastien

    ()
    (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium and ECORE)

Abstract

The increasing works on parameter instability, structural changes and regime switches lead to the natural research question whether the assumption of stationarity is appropriate to model volatility processes. Early econometric studies have provided testing procedures of covariance stationarity and have shown empirical evidence for the unconditional time-variation of the dependence structure of many financial time series.After a review of several econometric tests of covariance stationarity, this survey paper focuses on several attempts in the literature to model the time-varying second- order dependence of volatility time series. The approaches that are summarized in this discussion paper propose various specification for this time-varying dynamics. In some of them an explicit variation over time is suggested, such as in the spline GARCH model. Larger classes of nonstationary models have also been proposed, in which the variation of the parameters may be more general such as in the so-called locally stationary models. In another approach that is called “adaptive”, no explicit global model is assumed and local parametric model are adaptively fitted at each point over time. Multivariate extensions are also visited. A comparison of these approaches is proposed in this paper and some illustrations are provided on the two last decades of data of the Dow Jones Industrial Average index.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2011041.

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Date of creation: 01 Oct 2011
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Handle: RePEc:cor:louvco:2011041

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Keywords: volatility; locally stationary time series; multiplicative model; adaptive estimation;

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  1. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
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  5. Cristina Amado & Timo Teräsvirta, 2011. "Modelling Volatility by Variance Decomposition," NIPE Working Papers 01/2011, NIPE - Universidade do Minho.
  6. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," CORE Discussion Papers 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  9. Van Bellegem, Sebastien & von Sachs, Rainer, 2004. "Forecasting economic time series with unconditional time-varying variance," International Journal of Forecasting, Elsevier, vol. 20(4), pages 611-627.
  10. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
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  13. Silvennoinen, Annastiina & Teräsvirta, Timo, 2007. "Multivariate GARCH models," Working Paper Series in Economics and Finance 669, Stockholm School of Economics, revised 18 Jan 2008.
  14. Hafner, Christian M. & Linton, Oliver, 2010. "Efficient estimation of a multivariate multiplicative volatility model," Journal of Econometrics, Elsevier, vol. 159(1), pages 55-73, November.
  15. Hillebrand, Eric, 2005. "Neglecting parameter changes in GARCH models," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 121-138.
  16. Giuseppe Cavaliere, 2003. "Unit root tests under time-varying variances," Quaderni di Dipartimento 2, Department of Statistics, University of Bologna.
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  18. Francesco Audrino & Peter Bühlmann, 2009. "Splines for financial volatility," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 655-670.
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Cited by:
  1. Bonsoo Koo & Oliver Linton, 2013. "Let's get LADE: robust estimation of semiparametric multiplicative volatility models," CeMMAP working papers CWP11/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Amado, Cristina & Teräsvirta, Timo, 2013. "Modelling volatility by variance decomposition," Journal of Econometrics, Elsevier, vol. 175(2), pages 142-153.
  3. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," CORE Discussion Papers 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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