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Combining Long Memory and Level Shifts in Modeling and Forecasting the Volatility of Asset Returns

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  • Rasmus Tangsgaard Varneskov

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

  • Pierre Perron

    (Department of Economics, Boston University)

Abstract

We propose a parametric state space model with accompanying estimation and forecasting framework that combines long memory and level shifts by decomposing the underlying process into a simple mixture model and ARFIMA dynamics. The Kalman filter is used to construct the likelihood function after augmenting the probability of states by a mixture of normally distributed processes. The forecasts are constructed by exploiting the information in the Kalman recursions. The validity of the estimation methodology is shown through a comprehensive simulation study. Besides being able to identify the true memory of a process, the model consistently belongs to the 10% Model Confidence Set when considering out-of-sample forecasting performance as the only one among four competing dynamic models for all forecasting horizons when applied to high frequency stock- and bond market data together with time series of daily returns on stock market and exchange rate data. As a by-product, we provide simulation and empirical evidence of the "Spurious Break" phenomenon when estimating the number of level shifts in structural models for I(d) processes.

Suggested Citation

  • Rasmus Tangsgaard Varneskov & Pierre Perron, 2011. "Combining Long Memory and Level Shifts in Modeling and Forecasting the Volatility of Asset Returns," CREATES Research Papers 2011-26, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2011-26
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    More about this item

    Keywords

    Forecasting; Kalman Filter; Long Memory Processes; State Space Modeling; Structural Change.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: 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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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