Periodic autoregressive conditional duration

• Published in: Journal of time series analysis Vol. 43; no. 1; pp. 5 - 29
• Main Authors: Aknouche, Abdelhakim, Almohaimeed, Bader, Dimitrakopoulos, Stefanos
• Format: Journal Article
• Language: English
• Published: Oxford, UK John Wiley & Sons, Ltd 01.01.2022; Blackwell Publishing Ltd
• Subjects: Asymptotic properties; autoregressive conditional duration; Autoregressive models; exponential QMLE; Maximum likelihood estimates; multiplicative error models; Parameters; periodic time‐varying models; Positive time series; Trading; two‐stage Gamma QMLE. MOS subject classification: 62F05, 62F12, 62M10, 62M20, 91B84
• ISSN: 0143-9782; 1467-9892
• DOI: 10.1111/jtsa.12588

We propose an autoregressive conditional duration (ACD) model with periodic time‐varying parameters and multiplicative error form. We name this model periodic autoregressive conditional duration (PACD). First, we study the stability properties and the moment structures of it. Second, we estimate the model parameters, using (profile and two‐stage) Gamma quasi‐maximum likelihood estimates (QMLEs), the asymptotic properties of which are examined under general regularity conditions. Our estimation method encompasses the exponential QMLE, as a particular case. The proposed methodology is illustrated with simulated data and two empirical applications on forecasting Bitcoin trading volume and realized volatility. We found that the PACD produces better in‐sample and out‐of‐sample forecasts than the standard ACD.