Hawkes_Process_JAX

Hawkes Process MLE Inference Using JAX

Run python hawkes.py
Requires tick and JAX
Hawkes Process model for event modelling https://en.wikipedia.org/wiki/Hawkes_process

$$\lambda_i (t) = \mu_i + \sum_j \sum_{t_{jl} < t} \alpha_{ij} \omega \exp{ \omega (t - t_{jl} ) }$$

Loglikelihood is defineds as,

$$\sum_{n=1}^N {\log(\lambda_{i_{t_n}} (t_n) )} - \sum_i \int_0^T \lambda_i (t) dt$$

Before Optimization Negative Loglikelihood 268.909910517387
After Optimization Negative Loglikelihood 219.8147895512949
\mu True values [0.5 0.1 0.5]
\mu Estimated Values [0.53409991 0.04881035 0.4799496 ]
\alpha True values

$$[[0.1 0. 0. ] [0. 0.3 0. ] [0. 0. 0.5]]$$

\alpha Estimated Values

$$[[0.01708269 0. 0.04558697] [0.04051707 0.37785955 0. ] [0.07921349 0.2555025 0.53284138]]$$

\omega true value 0.3
\omega estimate value 0.22339805387220335