“…According to the literature, there are some possible shapes of intra-day patterns in various stock market characteristics such as volumes, depths, spreads, returns, transaction costs, order flows, market resiliency, etc. (see e.g., [ 55 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 ] and the references therein). Goodhart and O’Hara [ 58 ] emphasize that a fundamental property of high-frequency data is that observations can occur at varying time intervals.…”