Return direction forecasting: a conditional autoregressive shape model with beta density

This paper derives a new decomposition of stock returns using price extremes and proposes a conditional autoregressive shape (CARS) model with beta density to predict the direction of stock returns. The CARS model is continuously valued, which makes it different from binary classification models. An empirical study is performed on the US stock market, and the results show that the predicting power of the CARS model is not only statistically significant but also economically valuable. We also compare the CARS model with the probit model, and the results demonstrate that the proposed CARS model outperforms the probit model for return direction forecasting. The CARS model provides a new framework for return direction forecasting.