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Title: Forecasting in GARCH models with polynomially modified innovations Authors:  Gianmarco Vacca - Università Cattolica del Sacro Cuore (Italy) [presenting]
Maria Grazia Zoia - Catholic University of the Sacred Heart - Milan (Italy)
Luca Bagnato - Catholic University of the Sacred Heart (Italy)
Abstract: Orthogonal polynomials can be used to modify the moments of the distribution of a random variable. 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.