tick.hawkes.HawkesKernelPowerLaw

class tick.hawkes.HawkesKernelPowerLaw(multiplier, cutoff, exponent, support=-1, error=1e-05)[source]

Hawkes kernel for power law

\[\phi(t) = \phi(t) = \alpha (\delta + t)^{- \beta} 1_{t > 0}\]

Where \(\alpha\) is called the multiplier, delta the cut-off and \(\beta\) the exponent

Parameters

multiplier : float

Multiplier of the kernel, also noted \(\alpha\)

cutoff : float

Cut-off of the kernel, also noted \(\delta\)

exponent : float

Exponent of the kernel, also noted \(\beta\)

__init__(multiplier, cutoff, exponent, support=-1, error=1e-05)[source]

Initialize self. See help(type(self)) for accurate signature.

get_norm(n_steps=10000)

Computes L1 norm

Parameters

n_steps : int

number of steps used for integral discretization

Notes

By default it approximates Riemann sum with step-wise function. It might be overloaded if L1 norm closed formula exists

get_plot_support()

Returns support used to plot the kernel

get_support()

Returns the upperbound of the support

get_value(t)

Returns the value of the kernel at t

get_values(t_values)

Returns the value of the kernel for all times in t_values

is_zero()

Returns if this kernel is equal to 0