Fit a single (kernel, baseline) Hawkes specification — morie_tps_hawkes_advanced

Companion to the Markovian exponential / constant fit in morie_tps_hawkes_temporal_fit. Supports the four kernels (exponential, gamma, Weibull, Lomax) and two baselines (constant, sinusoidal) of Kwan-Chen-Dunsmuir (2024).

Usage

morie_tps_hawkes_advanced_fit(
  df,
  kernel = "gamma",
  baseline = "sinusoidal",
  ds_name = "?",
  max_n = 5000L
)

Arguments

df: A data frame with an OCC_DATE or REPORT_DATE column.
kernel: Excitation kernel: one of "exponential", "gamma", "weibull", "lomax".
baseline: Baseline kind: "constant" or "sinusoidal".
ds_name: Dataset name used in titles and warnings.
max_n: Maximum number of events to retain (for tractable O(n^2) MLE on the non-Markovian path).

Value

A morie_rich_result with branching ratio, stationarity verdict, kernel and baseline parameters, negative log-likelihood, AIC, BIC, and time-rescaling KS statistic.

Details

If the optional packages hawkes or emhawkes are available the (exponential, constant) special case can delegate to their compiled likelihood routines; the non-Markovian kernels always use the base-R O(n^2) negative log-likelihood with L-BFGS-B optimisation under explicit box constraints.

Goodness-of-fit is reported via time-rescaling residuals (Brown et al. 2002) and a Kolmogorov-Smirnov test against Uniform(0, 1).

References

Kwan TKJ, Chen F, Dunsmuir WTM (2024). Likelihood inference for non-stationary Hawkes processes. arXiv:2408.09710v1.

Examples

if (FALSE) { # \dontrun{
  df <- morie_tps_load_tps_dataset("Assault", nrows = 4000)
  rr <- morie_tps_hawkes_advanced_fit(df, kernel = "gamma",
                                        baseline = "sinusoidal",
                                        ds_name = "Assault")
  print(rr$summary_lines)
} # }