Volatility Information in High-Frequency Financial Interval-Valued Time Series: A Direct Modeling Pattern

The aim of this paper is to develop a forecasting method with global interval input and output for interval-valued financial time series by combining the VAR[Formula: see text] process, the volatility information and neural network, namely VAR-NN. To reflect the volatility information, four types of interval-valued data volatility information from both the relative and absolute perspectives are constructed. Furthermore, the neural network is combined to produce the parameters. The developed forecasting model is finally applied to the highest and lowest hourly prices of the Shanghai Composite Index prediction. Numerical study shows the feasibility and validity of the developed improved VAR model.