Daily return distribution forecast incorporating intraday high frequency information in China’s stock market

The stock market forecast is an important and challenging issue. Its distribution forecast of returns can provide information that is more complete, compared to point forecast and interval forecast. As intraday high-frequency information is available, we incorporate intraday returns into the predictive modelling of daily return distribution in two ways: realized volatility and scale calibration. Three parametric models, EGARCH, EGARCH-X, and realGARCH, and two nonparametric models, NP and realNP, are used. Our improved NP model, the realNP model, is based on intraday returns calibration. The results show that intraday information improves goodness-of-fit and forecasting effect, and the realGARCH model is relatively the best. According to the realNP model results, the intraday returns can only contribute about a 30% description of the daily distribution and less than 1% information for a one-step-ahead distribution forecast. Furthermore, three combinations are considered, and the log-score and CRPS combinations are found to have direction predictability and excess profitability statistically. The non-short-selling situation consistently has more excess profits than the short-selling situation, which implies that the non-short-selling rule protects investors. This study reveals the importance of incorporating intraday information and model combinations for stock market forecast modelling.