Exponential | R Documentation |
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) = \beta \exp(-\beta t) 1_{\{t \ge 0\}}.
Its vector of parameters must be of the form (\eta, \mu, \beta)
.
Both loglik
, its derivatives, and whittle
can be used with this reproduction kernel.
The kernel SymmetricExponential
has density function
h^\ast(t) = 0.5 \beta \exp(-\beta |t|).
Its vector of parameters must be of the form (\eta, \mu, \beta)
.
Only whittle
can be used with this reproduction kernel.
The kernel Gaussian
has density function
h^\ast(t) = \frac{1}{\sigma \sqrt{2\pi}}\exp\left(-\frac{(t-\nu)^2}{2\sigma^2}\right).
Its vector of parameters must be of the form (\eta, \mu, \nu, \sigma^2)
.
Only whittle
is available with this reproduction kernel.
The kernel PowerLaw
has density function
h^\ast(t) = \theta a^\theta (t+a)^{-\theta-1} 1_{\{\theta > 0 \}}.
Its vector of parameters must be of the form (\eta, \mu, \theta, a)
.
Both loglik
, its derivatives, and whittle
can be used with this reproduction kernel.
The kernels Pareto3
, Pareto2
and Pareto1
have density function
h_\theta^\ast(t) = \theta a^\theta t^{-\theta - 1} 1_{\{t > a\}},
with \theta
= 3, 2 and 1 respectively.
Their vectors of parameters must be of the form (\eta, \mu, a)
.
Only whittle
is available with this reproduction kernel.
Model
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.