Multivariate Hawkes processes: an application to financial data
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TLDR
The statistical estimation and goodness-of-fit are derived for multivariate Hawkes processes with possibly dependent marks and two data sets from finance are analyzed.Abstract:
A Hawkes process is also known under the name of a self-exciting point process and has numerous applications throughout science and engineering. We derive the statistical estimation (maximum likelihood estimation) and goodness-of-fit (mainly graphical) for multivariate Hawkes processes with possibly dependent marks. As an application, we analyze two data sets from finance.read more
Citations
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Journal ArticleDOI
Hawkes Processes in Finance
TL;DR: An overview of the recent academic literature devoted to the applications of Hawkes processes in finance can be found in this article, where the authors review their main empirical applications to address many different problems in high-frequency finance.
Journal ArticleDOI
Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data
TL;DR: A numerical method is defined that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes and finds slowly decaying (power-law) kernel shapes suggesting a long memory nature of self-excitation phenomena at the microstructure level of price dynamics.
Journal ArticleDOI
Some limit theorems for Hawkes processes and application to financial statistics
TL;DR: In this article, a functional central limit theorem was proved for multivariate Hawkes processes observed over a time interval [ 0, T ] when T?? is a discrete scheme with mesh? over [ 0, T ] up to some further time shift.
Journal ArticleDOI
Hawkes model for price and trades high-frequency dynamics
TL;DR: In this article, a multivariate Hawkes process is introduced to account for the dynamics of market prices through the impact of market order arrivals at microstructural level, which is a point process mainly characterized by four kernels associated with, respectively, the trade arrival self-excitation, the price changes mean reversion, impact of trade arrivals on price variations and the feedback of price changes on trading activity.
Posted Content
Critical reflexivity in financial markets: a Hawkes process analysis
TL;DR: In this paper, the arrival of mid-price changes in the E-Mini S&P futures contract was modeled as a self-exciting Hawkes process, and the Hawkes kernel was found to be power-law with a decay exponent close to -1.15 at short times, less than approximately 10^3 seconds, and cross over to a second power law regime with a larger decay exponent of approximately −1.45 for longer times scales in the range [10^3, 10^6] seconds.
References
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Book
Modelling Extremal Events: for Insurance and Finance
TL;DR: In this article, an approach to Extremes via Point Processes is presented, and statistical methods for Extremal Events are presented. But the approach is limited to time series analysis for heavy-tailed processes.
BookDOI
An introduction to the theory of point processes
Daryl J. Daley,David Vere-Jones +1 more
TL;DR: An introduction to the theory of point processes can be found in this article, where the authors introduce the concept of point process and point process theory and introduce point processes as a theory for point processes.
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Quantitative Risk Management: Concepts, Techniques, and Tools
TL;DR: The most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management can be found in this paper, where the authors describe the latest advances in the field, including market, credit and operational risk modelling.
Journal ArticleDOI
Spectra of some self-exciting and mutually exciting point processes
TL;DR: In this paper, the theoretical properties of a class of processes with particular reference to the point spectrum or corresponding covariance density functions are discussed and a particular result is a self-exciting process with the same second-order properties as a certain doubly stochastic process.