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A Moving Average Heterogeneous Autoregressive Model for Forecasting the Realized Volatility of the US Stock Market: Evidence from Over a Century of Data


  • Afees A. Salisu

    () (Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam and Faculty of Business Administration, Ton Duc Thang University, Ho Chi Minh City, Vietnam)

  • Rangan Gupta

    () (Department of Economics, University of Pretoria, Pretoria, 0002, South Africa)

  • Ahamuefula E. Ogbonna

    () (Centre for Econometric & Allied Research, University of Ibadan and Department of Statistics, University of Ibadan)


This study forecasts the monthly realized volatility of the US stock market covering the period of February, 1885 to September, 2019 using a recently developed novel approach – a moving average heterogeneous autoregressive (MAT-HAR) model, which treats threshold as a moving average generated time varying parameter rather than as a fixed or unknown parameter. The significance of asymmetric information in realized volatility of stock market forecasting is also considered by examining the case of good and bad realized volatility. The Clark and West (2007) forecast evaluation approach is employed to evaluate the forecast performance of the proposed predictive model vis-à-vis the conventional HAR and threshold HAR (T-HAR) models. We find evidence in favour of the MAT-HAR model relative to the HAR and T-HAR models. Also observed is the significant role of asymmetry in modeling the realized volatility as good realized volatility and bad realized volatility yield dissimilar predictability results. Our results are not sensitive to the choice of sample periods and realized volatility measures.

Suggested Citation

  • Afees A. Salisu & Rangan Gupta & Ahamuefula E. Ogbonna, 2019. "A Moving Average Heterogeneous Autoregressive Model for Forecasting the Realized Volatility of the US Stock Market: Evidence from Over a Century of Data," Working Papers 201978, University of Pretoria, Department of Economics.
  • Handle: RePEc:pre:wpaper:201978

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    References listed on IDEAS

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    More about this item


    Realized volatility; US stock market; Forecast evaluation; HAR models;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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