Module hawkes

Implements the Hawkes self-exciting jump process.

Structs

ExpKernel

Exponential kernel for the Hawkes process, of the form $$g(t) = \alpha \exp(-\beta t)$$

Hawkes

The Hawkes process is a self-exciting point process: the intensity process is stochastic and defined by $$ \lambda_t = \lambda_0(t) + \int_0^t g(t-s) dN_s $$ where $g$ is called the kernel of the Hawkes process.

PowerLawKernel

The power law kernel for the Hawkes process has the form $$ g(t) = \frac{\alpha}{(\delta + t)^\beta}$$

SumExpKernel

Sum-of-exponentials kernel, has the form: $$g(t) = \sum_{j=1}^p \alpha_j \exp(-\beta_j t)$$

Traits

Kernel

Kernel $g$ for the Hawkes process.

Type Aliases

ConstBackground

Constant background intensity $\lambda_0$ for the Hawkes process.

DeterministicBackground

Deterministic background intensity $\lambda_0(t)$

ExpHawkes

Hawkes model with an exponential kernel.

PowerLawHawkes

Hawkes model with a power-law kernel and constant background intensity.