Statistical analysis Dow Jones Stock Index: Cumulative return gap and finite difference method

This study was motivated by the poor performance of the current models used in stock return forecasting and aimed to improve the accuracy of the existing models in forecasting future stock returns. The current literature largely assumes that the residual term used in the existing model is white noise and, as such, has no valuable information. We exploit the valuable information contained in the residuals of the models in the context of cumulative return and construct a new cumulative return gap (CRG) model to overcome the weaknesses of the traditional cumulative abnormal returns (CAR) and buy-and-hold abnormal returns (BHAR) models. To deal with the residual items of the prediction model and improving the prediction accuracy, we also lead the finite difference (FD) method into the autoregressive (AR) model and autoregressive distributed lag (ARDL) model. The empirical results of the study show that the cumulative return (CR) model is better than the simple return model for stock return prediction. We found that the CRG model can improve prediction accuracy, the term of the residuals from the autoregressive analysis is very important in stock return prediction, and the FD model can improve prediction accuracy.