A flexible Sine Alpha Power Weibull ACD model

Abstract

High-frequency financial markets generate data at irregular intervals, and durations, defined as the elapsed time between successive market events play a key role in modeling market volatility and liquidity. Classical innovation distributions frequently fall short of capturing the heavy tails, skewness, and intricate conditional intensity patterns present in financial data, despite the Autoregressive Conditional Duration (ACD) model being a typical tool for modeling these temporal dependencies. Although the ACD model is frequently utilized to capture historical dependencies in financial data, classical innovation distributions often fail to adequately represent heavy tails, skewness, and complex conditional intensity patterns. To address this restriction, the Sine Alpha Power Weibull Autoregressive Conditional Duration (SAP–W–ACD) model was developed. This approach offers a flexible framework by incorporating the recently introduced Sine Alpha Power-G (SAP-G) family of distributions into a Weibull baseline. “This study offers an in-depth theoretical analysis, derived the model's PDF, CDF, Quantile function, and series expansions for raw moments.” We employed Maximum Likelihood Estimation (MLE) to determine the model parameters and confirm the numerical reliability of these estimators using Monte Carlo simulations. High-frequency exchange rate durations from Ethiopia, Kenya, and Somalia analyzed using the SAP–W–ACD model. In terms of log-likelihood and information criteria, the empirical results show that the SAP–W–ACD model performs much better than competing specifications, such as the Lomax-ACD, and Gompertz-ACD models. Tests on standardized residuals demonstrate that the model effectively accounts for duration clustering. Furthermore, conditional intensity analysis identifies a 'positive aging' effect within East African currency markets, indicating that the probability of a rate adjustment increases as the time between events increases.