Forecasting duration in high-frequency financial data using a self-exciting flexible residual point process

Battle Count: 97

Highly relevant to quantitative trading as it directly addresses forecasting interarrival times of mid-price changes in the limit order book, which is fundamental to market microstructure modeling, algorithmic execution timing, liquidity assessment, and high-frequency trading strategy design. The self-exciting structure captures the clustering behavior observed in real trading data, and the flexible residual distributions accommodate the heavy-tailed nature of ultra-high-frequency durations. The empirical results on AAPL data demonstrate practical forecasting improvements over standard Hawkes and ACD models.

Moderate to high complexity. Requires: (1) numerical inversion of the integrated intensity function Phi, (2) one-dimensional numerical integration for conditional expectations, (3) maximum likelihood estimation with recursive latent state updates, (4) rolling-window estimation scheme for intraday adaptation, (5) careful handling of the stability condition alpha < beta * mu_epsilon, and (6) implementation of multiple residual distributions (Gamma, generalized Gamma, Burr Type XII) with their respective PDFs and hazard functions. The Markov chain stability analysis is theoretical and does not require implementation for forecasting purposes.

The paper provides detailed mathematical formulations, parameter estimation procedures, and empirical setup (AAPL data, December 2022, rolling-window with 5000 observations). However, no code repository is provided, and the numerical integration for conditional expectations and the specific optimization routines are not fully specified. The model definitions are precise enough for reimplementation, but practical implementation details (e.g., optimizer settings, numerical integration methods) are limited.