Compensator-based estimating equations unify several moment methods for compact-memory multivariate Hawkes processes, delivering uniform high-probability O(sqrt(log T / T)) rates, asymptotic normality, and exact efficiency-loss quantification relative to the likelihood score.
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A new Hawkes autoregressive process combines Hawkes and autoregressive dynamics, with proofs of a stationary version, cluster representation, stability, and ergodicity.
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Optimal Estimating Equations for Compact-Memory Hawkes Processes
Compensator-based estimating equations unify several moment methods for compact-memory multivariate Hawkes processes, delivering uniform high-probability O(sqrt(log T / T)) rates, asymptotic normality, and exact efficiency-loss quantification relative to the likelihood score.
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Hawkes autoregressive processes: a new model for multiscale and heterogeneous processes
A new Hawkes autoregressive process combines Hawkes and autoregressive dynamics, with proofs of a stationary version, cluster representation, stability, and ergodicity.