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Modelling Changes in the Unconditional Variance of Long Stock Return Series

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Listed:
  • Cristina Amado

    () (University of Minho and NIPE)

  • Timo Teräsvirta

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

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 Teräsvirta, 2012. "Modelling Changes in the Unconditional Variance of Long Stock Return Series," CREATES Research Papers 2012-07, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2012-07
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    References listed on IDEAS

    as
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    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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