Forecasting in GARCH models with polynomially modified innovations

Gianmarco Vacca*, Maria Zoia, Luca Bagnato

*Autore corrispondente per questo lavoro

Risultato della ricerca: Contributo in rivistaArticolo in rivista


Orthogonal polynomials can be used to modify the moments of the distribution of a random variable. In this paper, polynomially adjusted distributions are employed to model the skewness and kurtosis of the conditional distributions of GARCH models. To flexibly capture the skewness and kurtosis of data, the distributions of the innovations that are polynomially reshaped include, besides the Gaussian, also leptokurtic laws such as the logistic and the hyperbolic secant. Modeling GARCH innovations with polynomially adjusted distributions can effectively improve the precision of the forecasts. This strategy is analyzed in GARCH models with different specifications for the conditional variance, such as the APARCH, the EGARCH, the Realized GARCH, and APARCH with time-varying skewness and kurtosis. An empirical application on different types of asset returns shows the good performance of these models in providing accurate forecasts according to several criteria based on density forecasting, downside risk, and volatility prediction.
Lingua originaleEnglish
pagine (da-a)117-141
Numero di pagine25
RivistaInternational Journal of Forecasting
Stato di pubblicazionePubblicato - 2021


  • GARCH models
  • Orthogonal polynomials
  • Volatility forecast
  • kurtosis
  • skewness


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