  In this work we investigate tick-by-tick data provided by the TRTH database
for several stocks on three different exchanges (Paris - Euronext, London and
Frankfurt - Deutsche B\"orse) and on a 5-year span. We use a simple algorithm
that helps the synchronization of the trades and quotes data sources, providing
enhancements to the basic procedure that, depending on the time period and the
exchange, are shown to be significant. We show that the analysis of the
performance of this algorithm turns out to be a a forensic tool assessing the
quality of the aggregated database: we are able to track through the data some
significant technical changes that occurred on the studied exchanges. We also
illustrate the fact that the choices made when reconstructing order flows have
consequences on the quantitative models that are calibrated afterwards on such
data. Our study also provides elements on the trade signature, and we are able
to give a more refined look at the standard Lee-Ready procedure, giving new
elements on the way optimal lags should be chosen when using this method. The
findings are in line with both financial reasoning and the analysis of an
illustrative Poisson model of the order flow.
