Package HawkesPyLib

HawkesPyLib is a python package for simulation, and inference of Hawkes processes.

The source code of the package can be found on github.

The package is structured into three main modules:

The module HawkesPyLib.core contains the functions underlying the simulation and fitting methods.

Notes

The inference module currently only supports model fitting using maximum likelihood estimation, and is using scipy's L-BFGS-B algorithm as its optimization routine.

Hawkes process simulation is done via Ogata's modified thinning algorithm. For more details on the simulation algorithm see algorithm 2 in (Ogata 1981).

The core simulation and estimation algorithms are optimized for speed by recursively calculating the state of the process and further accelerated by using numba's JIT compiler.

For more information on Hawkes processes, their simulation and inference find the references below.

References:

  • Hawkes, A. G. (1971). Spectra of some self-exciting and mutually exciting point processes. Biometrika, 58(1):83 90.

  • Ogata, Y. (1981). On lewis simulation method for point processes. IEEE transactions on information theory, 27(1):23 31.

  • Ozaki, T. (1979). Maximum likelihood estimation of hawkes self-exciting point processes. Annals of the Institute of Statistical Mathematics, 31(1):145 155.

  • C. Zhu, R. H. Byrd and J. Nocedal. L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization (1997), ACM Transactions on Mathematical Software, 23, 4, pp. 550 - 560.

  • Filimonov, V. and Sornette, D. (2015). Apparent criticality and calibration issues in the hawkes self-excited point process model: application to high-frequency finan- cial data. Quantitative Finance, 15(8):1293 1314.

Sub-modules

HawkesPyLib.core
HawkesPyLib.inference
HawkesPyLib.processes
HawkesPyLib.simulation