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.

Vacca, G., Zoia, M., Bagnato, L., Forecasting in GARCH models with polynomially modified innovations, <<INTERNATIONAL JOURNAL OF FORECASTING>>, 2022; 38 (1): 117-141. [doi:10.1016/j.ijforecast.2021.04.005] [http://hdl.handle.net/10807/189965]

Forecasting in GARCH models with polynomially modified innovations

Vacca, Gianmarco
Primo
Software
;
Zoia, Maria
Secondo
Methodology
;
Bagnato, Luca
Penultimo
Data Curation
2021

Abstract

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.
Inglese
Vacca, G., Zoia, M., Bagnato, L., Forecasting in GARCH models with polynomially modified innovations, <<INTERNATIONAL JOURNAL OF FORECASTING>>, 2022; 38 (1): 117-141. [doi:10.1016/j.ijforecast.2021.04.005] [http://hdl.handle.net/10807/189965]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/189965
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