90 research outputs found
The role of volume in order book dynamics: a multivariate Hawkes process analysis
We show that multivariate Hawkes processes coupled with the nonparametric
estimation procedure first proposed in Bacry and Muzy (2015) can be
successfully used to study complex interactions between the time of arrival of
orders and their size, observed in a limit order book market. We apply this
methodology to high-frequency order book data of futures traded at EUREX.
Specifically, we demonstrate how this approach is amenable not only to analyze
interplay between different order types (market orders, limit orders,
cancellations) but also to include other relevant quantities, such as the order
size, into the analysis, showing also that simple models assuming the
independence between volume and time are not suitable to describe the data
Linear processes in high-dimension: phase space and critical properties
In this work we investigate the generic properties of a stochastic linear
model in the regime of high-dimensionality. We consider in particular the
Vector AutoRegressive model (VAR) and the multivariate Hawkes process. We
analyze both deterministic and random versions of these models, showing the
existence of a stable and an unstable phase. We find that along the transition
region separating the two regimes, the correlations of the process decay
slowly, and we characterize the conditions under which these slow correlations
are expected to become power-laws. We check our findings with numerical
simulations showing remarkable agreement with our predictions. We finally argue
that real systems with a strong degree of self-interaction are naturally
characterized by this type of slow relaxation of the correlations.Comment: 40 pages, 5 figure
The nature of price returns during periods of high market activity
By studying all the trades and best bids/asks of ultra high frequency
snapshots recorded from the order books of a basket of 10 futures assets, we
bring qualitative empirical evidence that the impact of a single trade depends
on the intertrade time lags. We find that when the trading rate becomes faster,
the return variance per trade or the impact, as measured by the price variation
in the direction of the trade, strongly increases. We provide evidence that
these properties persist at coarser time scales. We also show that the spread
value is an increasing function of the activity. This suggests that order books
are more likely empty when the trading rate is high.Comment: 17 pages, 11 figure
Harmonic Decomposition of Audio Signals with Matching Pursuit
International audienceWe introduce a dictionary of elementary waveforms, called harmonic atoms, that extends the Gabor dictionary and fits well the natural harmonic structures of audio signals. By modifying the "standard" matching pursuit, we define a new pursuit along with a fast algorithm, namely, the fast harmonic matching pursuit, to approximate N-dimensional audio signals with a linear combination of M harmonic atoms. Our algorithm has a computational complexity of O(MKN), where K is the number of partials in a given harmonic atom. The decomposition method is demonstrated on musical recordings, and we describe a simple note detection algorithm that shows how one could use a harmonic matching pursuit to detect notes even in difficult situations, e.g., very different note durations, lots of reverberation, and overlapping notes
Market impacts and the life cycle of investors orders
In this paper, we use a database of around 400,000 metaorders issued by
investors and electronically traded on European markets in 2010 in order to
study market impact at different scales.
At the intraday scale we confirm a square root temporary impact in the daily
participation, and we shed light on a duration factor in with
. Including this factor in the fits reinforces the square
root shape of impact. We observe a power-law for the transient impact with an
exponent between (for long metaorders) and (for shorter ones).
Moreover we show that the market does not anticipate the size of the
meta-orders. The intraday decay seems to exhibit two regimes (though hard to
identify precisely): a "slow" regime right after the execution of the
meta-order followed by a faster one. At the daily time scale, we show price
moves after a metaorder can be split between realizations of expected returns
that have triggered the investing decision and an idiosynchratic impact that
slowly decays to zero.
Moreover we propose a class of toy models based on Hawkes processes (the
Hawkes Impact Models, HIM) to illustrate our reasoning.
We show how the Impulsive-HIM model, despite its simplicity, embeds appealing
features like transience and decay of impact. The latter is parametrized by a
parameter having a macroscopic interpretation: the ratio of contrarian
reaction (i.e. impact decay) and of the "herding" reaction (i.e. impact
amplification).Comment: 30 pages, 12 figure
Intermittent process analysis with scattering moments
Scattering moments provide nonparametric models of random processes with
stationary increments. They are expected values of random variables computed
with a nonexpansive operator, obtained by iteratively applying wavelet
transforms and modulus nonlinearities, which preserves the variance. First- and
second-order scattering moments are shown to characterize intermittency and
self-similarity properties of multiscale processes. Scattering moments of
Poisson processes, fractional Brownian motions, L\'{e}vy processes and
multifractal random walks are shown to have characteristic decay. The
Generalized Method of Simulated Moments is applied to scattering moments to
estimate data generating models. Numerical applications are shown on financial
time-series and on energy dissipation of turbulent flows.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1276 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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