Using CARR Model and GARCH Model to Forecast Volatility of the Stock Index: Evidence from China's Shanghai Stock Market

Generalized autoregressive conditional heteroscedasticity model (henceforth GARCH model) is a successful model for modeling and forecasting the volatility of financial market. But GARCH models use the closing price data of trading days to calculate the return on assets, without considering the asset price changes during the trading day. Especially when asset prices change greatly during the trading day, the volatility estimated by GARCH model is lower than real volatility. The conditional autoregressive range model (henceforth CARR model) use the range data, which is the difference between the highest asset price and lowest asset price during the trading day to study the volatility of asset prices. WCARR model can make full use of asset price change information during the trading day. We use the daily data of China's Shanghai composite index over the period 2002 to 2012 as the sample data and employ CARR model and GARCH model to model the volatility of Shanghai stock market in this paper. The empirical results show that both WCARR model and GARCH model do a great job in fitting the volatility of stock market. We use MZ regression equation, RMSE and MAE to compare the forecasting ability of WCARR model and GARCH-t model. The empirical results show that WCARR model is better than traditional GARCH model both in in-sample forecasting and out-of-sample forecasting.