If you compare a stock's price and volume in LOBSTER to some low frequency data source, such as Yahoo Finance, you may see a big difference sometimes. This is much more like to happen for several years ago data than several days ago. Does one of the data source get a wrong data? The answer is NO. Both data are correct. But how it comes?
The reason behind the discrepancy is mostly due to the corporate action adjustment. Almost all low frequency data sources provide the adjusted price, not the original price! Here is an example. Say a stock was sold 10000 @ $10.00 at the close auction five years ago and yesterday close was 10000 @ $100.00. This morning the corporate action of splitting 1 share to 10 took effect. The low frequency data source would have adjusted the price and volume accordingly on the ENTIRE historical period. So you would see yesterday's close auction as 100000 @ $10.00 and five years ago 100000 @ $1.00. On the other hand, LOBSTER data is constructed from original message tap from NASDAQ TotalView real time data feed. It always honestly represents what the traders saw on that day. No adjustment! Another reason we don't do the adjustment is (keep it as a secret!) applying the price/volume adjustment on LOBSTER original tap (more than 50TB binary data over a decade) would be a HUGE technical challenge!!!
Note that since many corporate actions could impact the price and volume (though, not value) of a stock. I will suggest researchers investigate the overnight price and volume time series first if their models are supposed to treat multiple-day data as one whole series. If there were clearly huge jumps (typically greater than 50%) overnight, please check the corporate action news by Google or Bloomberg.