Abstract: In this paper, a data-driven smooth test for in-sample and out-of-sample density forecast evaluation is developed, the Newey-Tauchen method and the West-McCracken method are applied separately to correct the effects of the parameter estimation on the in-sample and out-of-sample test statistics. Then, procedure proposed is applied to analyze the in-sample and the out-of-sample forecast performance of various maximum entropy GARCH models for three stock indexes-HSI、SHCI and TWII. The results justify that the maximum entropy GARCH model could be used to capture excess kurtosis, asymmetry and high peakedness generally observed in financial data, the Pearson type IV distribution which taking care of fat tail and skewed conditional distribution in GARCH-type models is of importance for the stock return density forecast. Moreover, it can be found that better in-sample goodness-of-fit and forecast performance does not imply better out-of-sample forecast performance.

Key words: density forecast evaluation, maximum entropy GARCH model, data-driven smooth test, probability integral transformation