These classes are derived from the class `Model`

, each implementing
a different reproduction kernel for the Hawkes process.
They inherit all fields from Model.

The kernel

`Exponential`

has density function*h^\ast(t) = β \exp(-β t) 1_{\{t ≥ 0\}}.*Its vector of parameters must be of the form

*(η, μ, β)*. Both`loglik`

, its derivatives, and`whittle`

can be used with this reproduction kernel.The kernel

`SymmetricExponential`

has density function*h^\ast(t) = 0.5 β \exp(-β |t|).*Its vector of parameters must be of the form

*(η, μ, β)*. Only`whittle`

can be used with this reproduction kernel.The kernel

`Gaussian`

has density function*h^\ast(t) = \frac{1}{σ √{2π}}\exp≤ft(-\frac{(t-ν)^2}{2σ^2}\right).*Its vector of parameters must be of the form

*(η, μ, ν, σ^2)*. Only`whittle`

is available with this reproduction kernel.The kernel

`PowerLaw`

has density function*h^\ast(t) = θ a^θ (t+a)^{-θ-1} 1_{\{θ > 0 \}}.*Its vector of parameters must be of the form

*(η, μ, θ, a)*. Both`loglik`

, its derivatives, and`whittle`

can be used with this reproduction kernel.The kernels

`Pareto3`

,`Pareto2`

and`Pareto1`

have density function*h_θ^\ast(t) = θ a^θ t^{-θ - 1} 1_{\{t > a\}},*with

*θ*= 3, 2 and 1 respectively. Their vectors of parameters must be of the form*(η, μ, a)*. Only`whittle`

is available with this reproduction kernel.

Model

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