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We present a large-scale study of commonality in liquidity and resilienceacross assets in an ultra high-frequency (millisecond-timestamped) Limit OrderBook (LOB) dataset from a pan-European electronic equity trading facility. Wefirst show that extant work in quantifying liquidity commonality through thedegree of explanatory power of the dominant modes of variation of liquidity(extracted through Principal Component Analysis) fails to account for heavytailed features in the data, thus producing potentially misleading results. Weemploy Independent Component Analysis, which both decorrelates the liquiditymeasures in the asset cross-section, but also reduces higher-order statisticaldependencies.  To measure commonality in liquidity resilience, we utilise a novelcharacterisation as the time required for return to a threshold liquiditylevel. This reflects a dimension of liquidity that is not captured by themajority of liquidity measures and has important ramifications forunderstanding supply and demand pressures for market makers in electronicexchanges, as well as regulators and HFTs. When the metric is mapped out acrossa range of thresholds, it produces the daily Liquidity Resilience Profile (LRP)for a given asset. This daily summary of liquidity resilience behaviour fromthe vast LOB dataset is then amenable to a functional data representation. Thisenables the comparison of liquidity resilience in the asset cross-section viafunctional linear sub-space decompositions and functional regression. Thefunctional regression results presented here suggest that market factors forliquidity resilience (as extracted through functional principal componentsanalysis) can explain between 10 and 40% of the variation in liquidityresilience at low liquidity thresholds, but are less explanatory at moreextreme levels, where individual asset factors take effect.

Liquidity commonality does not imply liquidity resilience commonality: A  functional characterisation for ultra-high frequency cross-sectional LOB data