This study introduces the Secant–Weibull Autoregressive Conditional Duration (SW–ACD) model and its extension with exogenous calendar effects (SW–ACD–X) . The primary innovation is the integration of the Secant-Weibull distribution as the innovation law, which allows the framework to capture non-monotonic intensity shapes, such as unimodal and bathtub patterns, that are typically inaccessible to standard monotonic models. A significant methodological contribution is the SW–ACD–X model, which endogenously incorporates intraday seasonality into the conditional mean equation. This joint estimation strategy provides an integrated alternative to traditional two-step pre-filtering by simultaneously capturing the interaction between deterministic diurnal patterns and stochastic duration clustering. The numerical properties of the proposed models are assessed through Monte Carlo simulations, which demonstrate asymptotic consistency while highlighting inherent identification challenges in small-sample regimes. Model estimation is implemented using a dual approach: Frequentist Maximum Likelihood and Bayesian Hamiltonian Monte Carlo (HMC) via the No-U-Turn Sampler (NUTS) in RStan. Empirical application to high-frequency IBM transaction data shows that the SW–ACD–X exhibits promising fit advantages over established benchmarks, including the W–ACD–X, LW–ACD–X, G-ACD-X , and Lomax–ACD–X models. Comprehensive model selection based on AIC, BIC, WAIC, and LOOIC confirms that the proposed model is a robust tool for analyzing market microstructure, liquidity dynamics, and the complex patterns of high-frequency durations.
