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.

中文翻译：

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周期性自回归条件持续时间

我们提出了一种具有周期性时变参数和乘法误差形式的自回归条件持续时间 (ACD) 模型。我们将此模型命名为周期性自回归条件持续时间 (PACD)。首先，我们研究了它的稳定性特性和力矩结构。其次，我们使用（剖面和两阶段）伽玛准最大似然估计（QMLE）估计模型参数，在一般规律条件下检查其渐近特性。作为特殊情况，我们的估计方法包括指数 QMLE。所提出的方法用模拟数据和两个预测比特币交易量和已实现波动率的经验应用来说明。我们发现 PACD 比标准 ACD 产生更好的样本内和样本外预测。