Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Liquidity commonality does not imply liquidity resilience commonality: A
  functional characterisation for ultra-high frequency cross-sectional LOB data   We present a large-scale study of commonality in liquidity and resilience
across assets in an ultra high-frequency (millisecond-timestamped) Limit Order
Book (LOB) dataset from a pan-European electronic equity trading facility. We
first show that extant work in quantifying liquidity commonality through the
degree of explanatory power of the dominant modes of variation of liquidity
(extracted through Principal Component Analysis) fails to account for heavy
tailed features in the data, thus producing potentially misleading results. We
employ Independent Component Analysis, which both decorrelates the liquidity
measures in the asset cross-section, but also reduces higher-order statistical
dependencies.
  To measure commonality in liquidity resilience, we utilise a novel
characterisation as the time required for return to a threshold liquidity
level. This reflects a dimension of liquidity that is not captured by the
majority of liquidity measures and has important ramifications for
understanding supply and demand pressures for market makers in electronic
exchanges, as well as regulators and HFTs. When the metric is mapped out across
a range of thresholds, it produces the daily Liquidity Resilience Profile (LRP)
for a given asset. This daily summary of liquidity resilience behaviour from
the vast LOB dataset is then amenable to a functional data representation. This
enables the comparison of liquidity resilience in the asset cross-section via
functional linear sub-space decompositions and functional regression. The
functional regression results presented here suggest that market factors for
liquidity resilience (as extracted through functional principal components
analysis) can explain between 10 and 40% of the variation in liquidity
resilience at low liquidity thresholds, but are less explanatory at more
extreme levels, where individual asset factors take effect.

1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol