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  • Forecasting Realized Volatilitywith Changing Average Levels

    Giampiero M. Gallo Edoardo OtrantoDipartimento di Statistica, Informatica, Applicazioni (DiSIA) G.Parenti Universit di FirenzeDipartimento di Scienze Cognitive e della Formazione andCRENoS Universit di Messina

    Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 1 / 49

  • Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 2 / 49

  • Outline

    Introduction

    On Todays Menu

    MEM and MSMEM

    Regimes in the Volatility of S&P500ModelingInference on RegimesIn and Outofsample Forecasting

    Extensions

    Conclusions

    Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 3 / 49

  • Persistence as a Challenge to Volatility Modeling

    BackgroundI Direct measurement of volatility: ideal properties of the

    estimators ex postI Modeling for forecasting purposes: dynamic modelsI Clustering features are presentI Choice of modeling volatility or logvolatilityI Residual diagnostics as a guideline to specificationI Possible recalcitrant residual correlation as a guide to

    misspecification

    Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 4 / 49

  • Persistence as a Challenge to Volatility Modeling

    BackgroundI Direct measurement of volatility: ideal properties of the

    estimators ex postI Modeling for forecasting purposes: dynamic modelsI Clustering features are presentI Choice of modeling volatility or logvolatilityI Residual diagnostics as a guideline to specificationI Possible recalcitrant residual correlation as a guide to

    misspecification

    Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 4 / 49

  • Persistence as a Challenge to Volatility Modeling

    BackgroundI Direct measurement of volatility: ideal properties of the

    estimators ex postI Modeling for forecasting purposes: dynamic modelsI Clustering features are presentI Choice of modeling volatility or logvolatilityI Residual diagnostics as a guideline to specificationI Possible recalcitrant residual correlation as a guide to

    misspecification

    Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 4 / 49

  • Persistence as a Challenge to Volatility Modeling

    BackgroundI Direct measurement of volatility: ideal properties of the

    estimators ex postI Modeling for forecasting purposes: dynamic modelsI Clustering features are presentI Choice of modeling volatility or logvolatilityI Residual diagnostics as a guideline to specificationI Possible recalcitrant residual correlation as a guide to

    misspecification

    Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 4 / 49

  • Persistence as a Challenge to Volatility Modeling

    BackgroundI Direct measurement of volatility: ideal properties of the

    estimators ex postI Modeling for forecasting purposes: dynamic modelsI Clustering features are presentI Choice of modeling volatility or logvolatilityI Residual diagnostics as a guideline to specificationI Possible recalcitrant residual correlation as a guide to

    misspecification

    Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 4 / 49

  • Persistence as a Challenge to Volatility Modeling

    BackgroundI Direct measurement of volatility: ideal properties of the

    estimators ex postI Modeling for forecasting purposes: dynamic modelsI Clustering features are presentI Choice of modeling volatility or logvolatilityI Residual diagnostics as a guideline to specificationI Possible recalcitrant residual correlation as a guide to

    misspecification

    Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 4 / 49

  • S&P500 volatility (Jan. 3, 2000 to Oct. 26, 2012)

    Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 5 / 49

  • Nonlinear Effects in VolatilityHow to model such a series

    I Underlying movements at low frequencyI A variety of interpretations/choices

    I Levels vs logs; Variance vs VolatilityI Long memory (ARFIMA on logvol; Andersen et al. 2003;)I Quasi long memory (HAR on log-vol: Corsi, 2009;

    extensions: McAleer and Medeiros, 2008)I Spline fitting (van Bellegem and von Sachs, 2004; Engle

    and Rangel, 2008; Brownlees and Gallo, 2010)I Markov Switching linear model on vol (Maheu and

    McCurdy, 2002)I Markov Switching and fractionally integrated dynamics

    (Bordignon and Raggi, 2010)I Smooth multiplicative component in a GARCH framework

    (Amado and Tersvirta, 2012)I Interpretation of the time-varying unconditional volatility

    (Engle and Rangel, 2008)Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 6 / 49

  • Nonlinear Effects in VolatilityHow to model such a series

    I Underlying movements at low frequencyI A variety of interpretations/choices

    I Levels vs logs; Variance vs VolatilityI Long memory (ARFIMA on logvol; Andersen et al. 2003;)I Quasi long memory (HAR on log-vol: Corsi, 2009;

    extensions: McAleer and Medeiros, 2008)I Spline fitting (van Bellegem and von Sachs, 2004; Engle

    and Rangel, 2008; Brownlees and Gallo, 2010)I Markov Switching linear model on vol (Maheu and

    McCurdy, 2002)I Markov Switching and fractionally integrated dynamics

    (Bordignon and Raggi, 2010)I Smooth multiplicative component in a GARCH framework

    (Amado and Tersvirta, 2012)I Interpretation of the time-varying unconditional volatility

    (Engle and Rangel, 2008)Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 6 / 49

  • Nonlinear Effects in VolatilityHow to model such a series

    I Underlying movements at low frequencyI A variety of interpretations/choices

    I Levels vs logs; Variance vs VolatilityI Long memory (ARFIMA on logvol; Andersen et al. 2003;)I Quasi long memory (HAR on log-vol: Corsi, 2009;

    extensions: McAleer and Medeiros, 2008)I Spline fitting (van Bellegem and von Sachs, 2004; Engle

    and Rangel, 2008; Brownlees and Gallo, 2010)I Markov Switching linear model on vol (Maheu and

    McCurdy, 2002)I Markov Switching and fractionally integrated dynamics

    (Bordignon and Raggi, 2010)I Smooth multiplicative component in a GARCH framework

    (Amado and Tersvirta, 2012)I Interpretation of the time-varying unconditional volatility

    (Engle and Rangel, 2008)Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 6 / 49

  • Nonlinear Effects in VolatilityHow to model such a series

    I Underlying movements at low frequencyI A variety of interpretations/choices

    I Levels vs logs; Variance vs VolatilityI Long memory (ARFIMA on logvol; Andersen et al. 2003;)I Quasi long memory (HAR on log-vol: Corsi, 2009;

    extensions: McAleer and Medeiros, 2008)I Spline fitting (van Bellegem and von Sachs, 2004; Engle

    and Rangel, 2008; Brownlees and Gallo, 2010)I Markov Switching linear model on vol (Maheu and

    McCurdy, 2002)I Markov Switching and fractionally integrated dynamics

    (Bordignon and Raggi, 2010)I Smooth multiplicative component in a GARCH framework

    (Amado and Tersvirta, 2012)I Interpretation of the time-varying unconditional volatility

    (Engle and Rangel, 2008)Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 6 / 49

  • Nonlinear Effects in VolatilityHow to model such a series

    I Underlying movements at low frequencyI A variety of interpretations/choices

    I Levels vs logs; Variance vs VolatilityI Long memory (ARFIMA on logvol; Andersen et al. 2003;)I Quasi long memory (HAR on log-vol: Corsi, 2009;

    extensions: McAleer and Medeiros, 2008)I Spline fitting (van Bellegem and von Sachs, 2004; Engle

    and Rangel, 2008; Brownlees and Gallo, 2010)I Markov Switching linear model on vol (Maheu and

    McCurdy, 2002)I Markov Switching and fractionally integrated dynamics

    (Bordignon and Raggi, 2010)I Smooth multiplicative component in a GARCH framework

    (Amado and Tersvirta, 2012)I Interpretation of the time-varying unconditional volatility

    (Engle and Rangel, 2008)Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 6 / 49

  • Nonlinear Effects in VolatilityHow to model such a series

    I Underlying movements at low frequencyI A variety of interpretations/choices

    I Levels vs logs; Variance vs VolatilityI Long memory (ARFIMA on logvol; Andersen et al. 2003;)I Quasi long memory (HAR on log-vol: Corsi, 2009;

    extensions: McAleer and Medeiros, 2008)I Spline fitting (van Bellegem and von Sachs, 2004; Engle

    and Rangel, 2008; Brownlees and Gallo, 2010)I Markov Switching linear model on vol (Maheu and

    McCurdy, 2002)I Markov Switching and fractionally integrated dynamics

    (Bordignon and Raggi, 2010)I Smooth multiplicative component in a GARCH framework

    (Amado and Tersvirta, 2012)I Interpretation of the time-varying unconditional volatility

    (Engle and Rangel, 2008)Gallo & Otranto Changing Average Volatility Paris, Mar 30, 2015 6 / 49

  • Nonlinear Effects in VolatilityHow to model such a series

    I Underlying movements at low frequencyI A variety of interpretations/choices

    I Levels vs logs; Variance vs VolatilityI Long memory (ARFIMA on logvol; Andersen et al. 2003;)I Quasi long memory (HAR on log-vol: Corsi, 2009;

    extensions: McAleer and Medeiros, 2008)I Spline fitting (van Bellegem and von Sachs, 2004; Engle

    and Rangel, 2008; Brownlees and Gallo, 2010)I Markov Switching linear model on vol (Maheu and

    McCurdy, 2002)I Markov Switching and fractionally integrated dynamics

    (Bordignon and Raggi, 2010)I Smooth multiplicative component in a GARCH framework

    (Amado and Tersvirta, 2012)I Interpretation of the time-varying uncondit

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