Functional Volatility Relationship Analysis and Prediction in International Crude Oil Futures Markets

To measure intraday volatility in international crude oil futures markets, we use the functional conditional variance to measure volatility and focus on volatility relationship analysis and prediction. This paper analyzes the simultaneous and predictive volatility relationships in crude oil futures markets. For covariate markets with significantly positive predictive volatility relationships, this paper empirically extends the fGARCH-X model so that it can introduce the volatility characteristics of covariate markets. The empirical application shows that using the fGARCH-X model can generally improve the predictive effects of functional volatility in crude oil futures markets. The robustness results indicate that the improvement in volatility prediction is significant. This study is beneficial for the stable development of international crude oil futures markets and is valuable for investors' investment decision-making.