The article explores using different types of distributions to improve forecasting in GARCH models. By adjusting the shape of the distributions with polynomials, the models can better capture the skewness and kurtosis of the data. This method enhances forecast accuracy for various GARCH model specifications, including those with time-varying skewness and kurtosis. Empirical tests on asset returns demonstrate the effectiveness of this approach in providing precise forecasts for volatility and downside risk.