722 research outputs found
Modeling high frequency data using hawkes processes with power-law kernels
Those empirical properties exhibited by high frequency financial data, such as time-varying intensities and self-exciting features, make it a challenge to model appropriately the dynamics associated with, for instance, order arrival. To capture the microscopic structures pertaining to limit order books, this paper focuses on modeling high frequency financial data using Hawkes processes. Specifically, the model with power-law kernels is compared with the counterpart with exponential kernels, on the goodness of fit to the empirical data, based on a number of proposed quantities for statistical tests. Based on one-trading-day data of one representative stock, it is shown that Hawkes processes with power-law kernels are able to reproduce the intensity of jumps in the price processes more accurately, which suggests that they could serve as a realistic model for high frequency data on the level of microstructure
The limits of statistical significance of Hawkes processes fitted to financial data
Many fits of Hawkes processes to financial data look rather good but most of
them are not statistically significant. This raises the question of what part
of market dynamics this model is able to account for exactly. We document the
accuracy of such processes as one varies the time interval of calibration and
compare the performance of various types of kernels made up of sums of
exponentials. Because of their around-the-clock opening times, FX markets are
ideally suited to our aim as they allow us to avoid the complications of the
long daily overnight closures of equity markets. One can achieve statistical
significance according to three simultaneous tests provided that one uses
kernels with two exponentials for fitting an hour at a time, and two or three
exponentials for full days, while longer periods could not be fitted within
statistical satisfaction because of the non-stationarity of the endogenous
process. Fitted timescales are relatively short and endogeneity factor is high
but sub-critical at about 0.8
Uncovering Causality from Multivariate Hawkes Integrated Cumulants
We design a new nonparametric method that allows one to estimate the matrix
of integrated kernels of a multivariate Hawkes process. This matrix not only
encodes the mutual influences of each nodes of the process, but also
disentangles the causality relationships between them. Our approach is the
first that leads to an estimation of this matrix without any parametric
modeling and estimation of the kernels themselves. A consequence is that it can
give an estimation of causality relationships between nodes (or users), based
on their activity timestamps (on a social network for instance), without
knowing or estimating the shape of the activities lifetime. For that purpose,
we introduce a moment matching method that fits the third-order integrated
cumulants of the process. We show on numerical experiments that our approach is
indeed very robust to the shape of the kernels, and gives appealing results on
the MemeTracker database
Nonparametric Markovian Learning of Triggering Kernels for Mutually Exciting and Mutually Inhibiting Multivariate Hawkes Processes
In this paper, we address the problem of fitting multivariate Hawkes
processes to potentially large-scale data in a setting where series of events
are not only mutually-exciting but can also exhibit inhibitive patterns. We
focus on nonparametric learning and propose a novel algorithm called MEMIP
(Markovian Estimation of Mutually Interacting Processes) that makes use of
polynomial approximation theory and self-concordant analysis in order to learn
both triggering kernels and base intensities of events. Moreover, considering
that N historical observations are available, the algorithm performs
log-likelihood maximization in operations, while the complexity of
non-Markovian methods is in . Numerical experiments on simulated
data, as well as real-world data, show that our method enjoys improved
prediction performance when compared to state-of-the art methods like MMEL and
exponential kernels
- …