Abstract: Limited attention theory points out that investors have limited attention and can't possess all the information in the financial market. This will cause temporarily mispricing of stocks which generates volatility in the market, thus investor attention may include valuable information about future volatility.
Since the Baidu index can well measure active investor attention in China, the logistic smooth transition structure is incorporated in the heterogeneous autoregressive (HAR) models of realized volatility, with the Baidu index being the transition variable, which can characterize the nonlinear influence of investor attention variation on future volatility. Three HAR models are considered as the benchmark model, that is, the basic HAR-RV model, the HAR-RV-J model which includes jumps and the HAR-RV-CJ model with separates the contribution of continuous volatility and jumps.
50 ETF high-frequency data and the Baidu index from January 2, 2014 to November 30, 2017 are used as empirical data. For the out-of-sample forecast comparison, we not only compare the average losses, but also perform the Diebold-Mariano test and the model confidence set test to evaluate the statistical significance of the models' forecasting performance difference. Empirical results show that, the new models are significantly superior to the original heterogeneous autoregressive models both in-sample and out-of-sample, indicating that the nonlinear introduction of investor attention has significant contribution to volatility forecasting. In addition, compared to introducing the total index and the mobile index, introducing the PC oriented index contributes to volatility forecasting more significantly, showing that the investor attention represented by the PC oriented index impacts the market volatility more significantly.
The volatility forecasting capability is effectively improved by the nonlinear introduction of investor attention, and the appropriate choice of investor attention proxy is illuminated. Meanwhile, it provides practical guides for investor risk management and investment decision-making.

Key words: HAR models, logistic smooth transition, the Baidu index, investor attention, MCS test