Let assume that we have one month of tick data which were traded at NYSE. We want to model the price changes as a function of the last p lags of price changes and the last q lags of the time duration between trades ( this is similar to the GARMA(p,q) model). Each day we use the data from 9:30 until 16:00. My question is: in order to analyze the data should I analyze each day separately?
Probably yes. There is a time gap between the two days. During that time gap it's likely that there was a market being made (and trading going on) for that security outside of what your data captures. If there was no market and no relevant news or market movement taking place in between days, then you could argue for keeping the data together.