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Modelling Changes in the Unconditional Variance of Long Stock Return Series

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  • Cristina Amado

    () (Universidade do Minho - NIPE)

  • Timo Terasvirta

    () (CREATES, Department of Economics and Business, Aarhus University)

Abstract

In this paper we develop a testing and modelling procedure for describing the long-term volatility movements over very long return series. For the purpose, we assume that volatility is multiplicatively decomposed into a conditional and an unconditional component as in Amado and Teräsvirta (2011). The latter component is modelled by incorporating smooth changes so that the unconditional variance is allowed to evolve slowly over time. Statistical inference is used for specifying the parameterization of the time-varying component by applying a sequence of Lagrange multiplier tests. The model building procedure is illustrated with an application to daily returns of the Dow Jones Industrial Average stock index covering a period of more than ninety years. The main conclusions are as follows. First, the LM tests strongly reject the assumption of constancy of the unconditional variance. Second, the results show that the long-memory property in volatility may be explained by ignored changes in the unconditional variance of the long series. Finally, based on a formal statistical test we find evidence of the superiority of volatility forecast accuracy of the new model over the GJR-GARCH model at all horizons for a subset of the long return series.

Suggested Citation

  • Cristina Amado & Timo Terasvirta, 2012. "Modelling Changes in the Unconditional Variance of Long Stock Return Series," NIPE Working Papers 02/2012, NIPE - Universidade do Minho.
  • Handle: RePEc:nip:nipewp:02/2012
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    References listed on IDEAS

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    Cited by:

    1. Hanck, Christoph & Demetrescu, Matei & Kruse, Robinson, 2015. "Fixed-b Asymptotics for t-Statistics in the Presence of Time-Varying Volatility," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112916, Verein für Socialpolitik / German Economic Association.
    2. Cavaliere, Giuseppe & Nielsen, Morten Ørregaard & Taylor, A.M. Robert, 2017. "Quasi-maximum likelihood estimation and bootstrap inference in fractional time series models with heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 198(1), pages 165-188.
    3. Xu, Ke-Li, 2013. "Power monotonicity in detecting volatility levels change," Economics Letters, Elsevier, vol. 121(1), pages 64-69.
    4. Demetrescu, Matei & Kruse, Robinson, 2015. "Testing heteroskedastic time series for normality," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113221, Verein für Socialpolitik / German Economic Association.
    5. Silvennoinen Annastiina & Teräsvirta Timo, 2016. "Testing constancy of unconditional variance in volatility models by misspecification and specification tests," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(4), pages 347-364, September.
    6. Shi, Yanlin & Ho, Kin-Yip, 2015. "Modeling high-frequency volatility with three-state FIGARCH models," Economic Modelling, Elsevier, vol. 51(C), pages 473-483.
    7. Alessandra Amendola & Vincenzo Candila & Antonio Scognamillo, 2017. "On the influence of US monetary policy on crude oil price volatility," Empirical Economics, Springer, vol. 52(1), pages 155-178, February.
    8. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94 Edward Elgar Publishing.
    9. Pape, Katharina & Wied, Dominik & Galeano, Pedro, 2016. "Monitoring multivariate variance changes," Journal of Empirical Finance, Elsevier, vol. 39(PA), pages 54-68.
    10. Ke-Li Xu & Jui-Chung Yang, 2015. "Towards Uniformly Efficient Trend Estimation Under Weak/Strong Correlation and Non-stationary Volatility," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 63-86, March.
    11. Yves Dominicy & Harry-Paul Vander Elst, 2015. "Macro-Driven VaR Forecasts: From Very High to Very Low Frequency Data," Working Papers ECARES ECARES 2015-41, ULB -- Universite Libre de Bruxelles.
    12. Matei Demetrescu & Christoph Hanck & Robinson Kruse, 2016. "Fixed-b Inference in the Presence of Time-Varying Volatility," CREATES Research Papers 2016-01, Department of Economics and Business Economics, Aarhus University.
    13. Proietti, Tommaso, 2014. "Exponential Smoothing, Long Memory and Volatility Prediction," MPRA Paper 57230, University Library of Munich, Germany.
    14. repec:spr:compst:v:32:y:2017:i:3:d:10.1007_s00180-016-0687-x is not listed on IDEAS
    15. 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.
    16. Ke Zhu, 2018. "Statistical inference for autoregressive models under heteroscedasticity of unknown form," Papers 1804.02348, arXiv.org.
    17. Escribano, Alvaro & Sucarrat, Genaro, 2016. "Equation-by-Equation Estimation of Multivariate Periodic Electricity Price Volatility," MPRA Paper 72736, University Library of Munich, Germany.
    18. Paulo M.M. Rodrigues & Matei Demetrescu, 2016. "Residual-augmented IVX predictive regression," Working Papers w201605, Banco de Portugal, Economics and Research Department.
    19. Isao Ishida & Virmantas Kvedaras, 2015. "Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity," Econometrics, MDPI, Open Access Journal, vol. 3(1), pages 1-53, January.
    20. Hossein Asgharian & Charlotte Christiansen & Ai Jun Hou & Weining Wang, 0610. "Long- and Short-Run Components of Factor Betas: Implications for Equity Pricing," CREATES Research Papers 2017-34, Department of Economics and Business Economics, Aarhus University.
    21. Laurie Davies & Walter Kraemer, 2016. "Stylized Facts and Simulating Long Range Financial Data," CESifo Working Paper Series 5796, CESifo Group Munich.
    22. Cristina Amado & Annastiina Silvennoinen & Timo Terasvirta, 2017. "Modelling and Forecasting WIG20 Daily Returns," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 9(3), pages 173-200, September.
    23. Annastiina Silvennoinen & Timo Teräsvirta, 3108. "Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model," CREATES Research Papers 2017-28, Department of Economics and Business Economics, Aarhus University.
    24. Giampiero M. Gallo & Edoardo Otranto, 2017. "Combining Sharp and Smooth Transitions in Volatility Dynamics: a Fuzzy Regime Approach," Econometrics Working Papers Archive 2017_05, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    25. Laurie Davies & Walter Kramer, 2016. "Stylized Facts and Simulating Long Range Financial Data," Papers 1612.05229, arXiv.org.

    More about this item

    Keywords

    Model specification; Conditional heteroskedasticity; Lagrange multiplier test; Timevarying unconditional variance; Long financial time series; Volatility persistence;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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