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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