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We test three common information criteria (IC) for selecting the order of a Hawkes process with an intensity kernel that can be expressed as a mixture of exponential terms. These processes find application in high-frequency financial data…

Statistical Finance · Quantitative Finance 2017-04-05 J. M. Chen , A. G. Hawkes , E. Scalas , M. Trinh

Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, neuroscience, social networks,…

Probability · Mathematics 2018-10-02 Xuefeng Gao , Lingjiong Zhu

We investigate the behavior of limit order books on the meso-scale motivated by order execution scheduling algorithms. To do so we carry out empirical analysis of the order flows from market and limit order submissions, aggregated from…

Trading and Market Microstructure · Quantitative Finance 2017-08-10 Kyle Bechler , Michael Ludkovski

This paper extends the analysis of Muni Toke and Yoshida (2020) to the case of marked point processes. We consider multiple marked point processes with intensities defined by three multiplicative components, namely a common baseline…

Trading and Market Microstructure · Quantitative Finance 2022-01-04 Ioane Muni Toke , Nakahiro Yoshida

We introduce a point process regression model that is applicable to price models and limit order book models. Hawkes type autoregression in the intensity process is generalized to a stochastic regression to covariate processes. We establish…

Statistics Theory · Mathematics 2015-12-08 Teppei Ogihara , Nakahiro Yoshida

High-frequency market making is a liquidity-providing trading strategy that simultaneously generates many bids and asks for a security at ultra-low latency while maintaining a relatively neutral position. The strategy makes a profit from…

Computational Engineering, Finance, and Science · Computer Science 2021-10-01 Pankaj Kumar

We introduce a new model in order to describe the fluctuation of tick-by-tick financial time series. Our model, based on marked point process, allows us to incorporate in a unique process the duration of the transaction and the…

Trading and Market Microstructure · Quantitative Finance 2012-11-21 Alexis Fauth , Ciprian A. Tudor

The paper constructs a multi-variate Hawkes process model of Bitcoin block arrivals and price jumps. Hawkes processes are selfexciting point processes that can capture the self- and cross-excitation effects of block mining and Bitcoin price…

Networking and Internet Architecture · Computer Science 2022-04-01 Rui Luo , Vikram Krishnamurthy , Erik Blasch

Self-exciting processes of Hawkes type have been used to model various phenomena including earthquakes, neural activities, and views of online videos. Studies of temporal networks have revealed that sequences of social interevent times for…

Physics and Society · Physics 2015-06-05 Naoki Masuda , Taro Takaguchi , Nobuo Sato , Kazuo Yano

We propose a modeling framework for the dynamics of a reduced form order book in event time and based on event sizes. Our framework for the order book is influenced by [9], but compared to [9] we allow the best bid ask spread to be larger…

Probability · Mathematics 2014-02-21 Kaj Nyström , Sidi Mohamed Ould Aly

We study the optimal Market Making problem in a Limit Order Book (LOB) market simulated using a high-fidelity, mutually exciting Hawkes process. Departing from traditional Brownian-driven mid-price models, our setup captures key…

Trading and Market Microstructure · Quantitative Finance 2025-11-03 Konark Jain , Nick Firoozye , Jonathan Kochems , Philip Treleaven

We propose an actionable calibration procedure for general Quadratic Hawkes models of order book events (market orders, limit orders, cancellations). One of the main features of such models is to encode not only the influence of past events…

Trading and Market Microstructure · Quantitative Finance 2020-05-13 Antoine Fosset , Jean-Philippe Bouchaud , Michael Benzaquen

Traditionally, Hawkes processes are used to model time--continuous point processes with history dependence. Here we propose an extended model where the self--effects are of both excitatory and inhibitory type and follow a Gaussian Process.…

Machine Learning · Statistics 2021-05-21 Noa Malem-Shinitski , Cesar Ojeda , Manfred Opper

In classical Hawkes process, the baseline intensity and triggering kernel are assumed to be a constant and parametric function respectively, which limits the model flexibility. To generalize it, we present a fully Bayesian nonparametric…

Machine Learning · Computer Science 2019-10-30 Feng Zhou , Zhidong Li , Xuhui Fan , Yang Wang , Arcot Sowmya , Fang Chen

The Tick library allows researchers in market microstructure to simulate and learn Hawkes process in high-frequency data, with optimized parametric and non-parametric learners. But one challenge is to take into account the correct causality…

Machine Learning · Statistics 2021-01-19 Marcos Costa Santos Carreira

In this paper, we use the Hawkes process to model the sequence of failure, i.e., events of compressor station and conduct survival analysis on various failure events of the compressor station. However, until now, nearly all relevant…

Machine Learning · Computer Science 2021-12-28 Lu-ning Zhang , Jian-wei Liu , Xin Zuo

We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson…

Trading and Market Microstructure · Quantitative Finance 2011-06-29 Fabien Guilbaud , Huyen Pham

Multivariate Hawkes processes are a widely used class of self-exciting point processes, but maximum likelihood estimation naively scales as $O(N^2)$ in the number of events. The canonical linear exponential Hawkes process admits a faster…

Machine Learning · Computer Science 2026-05-07 Ahmer Raza , Hudson Smith

Many networks have event-driven dynamics (such as communication, social media and criminal networks), where the mean rate of the events occurring at a node in the network changes according to the occurrence of other events in the network.…

Social and Information Networks · Computer Science 2023-03-22 Santitissadeekorn N. , Delahaies S. , Lloyd D. J. B

The self-exciting Hawkes process is widely used to model events which occur in bursts. However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion. The presence of such…

Applications · Statistics 2021-06-03 Isabella Deutsch , Gordon J. Ross
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