  In this paper we investigate the endogenous information contained in four
liquidity variables at a five minutes time scale on equity markets around the
world: the traded volume, the bid-ask spread, the volatility and the volume at
first limits of the orderbook. In the spirit of Granger causality, we measure
the level of information by the level of accuracy of linear autoregressive
models. This empirical study is carried out on a dataset of more than 300
stocks from four different markets (US, UK, Japan and Hong Kong) from a period
of over five years. We discuss the obtained performances of autoregressive (AR)
models on stationarized versions of the variables, focusing on explaining the
observed differences between stocks.
  Since empirical studies are often conducted at this time scale, we believe it
is of paramount importance to document endogenous dynamics in a simple
framework with no addition of supplemental information. Our study can hence be
used as a benchmark to identify exogenous effects. On the other hand, most
optimal trading frameworks (like the celebrated Almgren and Chriss one), focus
on computing an optimal trading speed at a frequency close to the one we
consider. Such frameworks very often take i.i.d. assumptions on liquidity
variables; this paper document the auto-correlations emerging from real data,
opening the door to new developments in optimal trading.
