An empirical model of daily highs and lows

We construct an empirical model for daily highs and daily lows of US stock indexes based on the intuition that highs and lows do not drift apart over time. Our empirical results show that daily highs and lows of three main US stock price indexes are cointegrated. Data on openings, closings, and trading volume are found to offer incremental explanatory power for variations in highs and lows within the VECM framework. With all these variables, the augmented VECM models explain 40% to 50% of variations in daily highs and lows. The generalized impulse response analysis shows that the responses of daily highs and daily lows to the shocks depend on whether data on openings, closings, and trading volume are included in the analysis.