Discrete Hawkes Generator

A dicrete Hawkes process is characterized by its discrete time intensity rate $\lambda_t$, $t \in \mathbb{N}_+$,

$$\lambda_t = \mu(t) + \sum_{t' < t} \beta e^{- \beta (t - t')}.$$

Usage

• Initialized model with ${\tt beta}$ and ${\tt mu \textunderscore config}$, which describes the value of the parameters of the discrete Hawkes process (see equation above).
• ${\tt simulate()}$ : Simulate a trajectory of event occurance of length $\tt t$. A list of intensity rates ${\tt lam}$ is returned as the output. One can also set parameter ${\tt plot = True}$ to automatically visualize the simulated trajectory.
• ${\tt generate()}$ : Given previous trajectory ${\tt prev \textunderscore traj}$, generate future trajectory of length ${\tt t}$.
• ${\tt plot \textunderscore mu()}$ : Plot the base intensity rate $\mu(t)$ on $[0, {\tt t}]$.

Demos for the plots are shown below.