ANALYTICAL EVALUATION OF VOLATILITY FORECASTS

Authors

  • Torben G. Andersen,

    1. Northwestern University and National Bureau of Economic Research; Duke University and National Bureau of Economic Research; Université de Montréal (CIRANO, CIREQ), Canada
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  • Tim Bollerslev,

    1. Northwestern University and National Bureau of Economic Research; Duke University and National Bureau of Economic Research; Université de Montréal (CIRANO, CIREQ), Canada
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  • Nour Meddahi

    1. Northwestern University and National Bureau of Economic Research; Duke University and National Bureau of Economic Research; Université de Montréal (CIRANO, CIREQ), Canada
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    Abstract

    Estimation and forecasting for realistic continuous-time stochastic volatility models is hampered by the lack of closed-form expressions for the likelihood. In response, Andersen, Bollerslev, Diebold, and Labys (Econometrica, 71 (2003), 579–625) advocate forecasting integrated volatility via reduced-form models for the realized volatility, constructed by summing high-frequency squared returns. Building on the eigenfunction stochastic volatility models, we present analytical expressions for the forecast efficiency associated with this reduced-form approach as a function of sampling frequency. For popular models like GARCH, multifactor affine, and lognormal diffusions, the reduced form procedures perform remarkably well relative to the optimal (infeasible) forecasts.

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