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I am wanting to know if there is any standard approach for the following situation:

We receive trade and order book data over a connection from an exchange and are interested in downsampling this into BBO+trade data. However, since there is latency involved and trades can be received before or after the corresponding changes to the order book, how do we match the most recent past trade with the BBO data like is usually done with TAQ data?

Do we do try to keep everything in the order that it was recorded as being executed by the exchange ("exchange time") even if this means we don't use the most current data? (e.g., we receive the last X trades that occurred in order and then receive a BBO update, but it turns out that the exchange time of the BBO update is before the exchange time of the most recent trade, so we have to use the trade before that to pair with the corresponding BBO update).

Or do we do something such as just working in the order that we receive the data ("local time") meaning that we can sometimes have the "most recent past trade" actually having occurred after the most recent BBO update in exchange time but having occurred before the most recent BBO update if we use "local time"?

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