Using density forecast evaluation techniques, we compare the predictive performance of econometric specifications that have been developed for modeling duration processes in intra-day financial markets. The model portfolio encompasses various variants of the Autoregressive Conditional Duration (ACD) model and recently proposed dynamic factor models. The evaluation is conducted on time series of trade, price and volume durations computed from transaction data of NYSE listed stocks. The results show that simpler approaches perform at least as well as more complex methods. With respect to modeling trade duration processes, standard ACD models successfully account for duration dynamics while none of the models provides an acceptable specification for the conditional duration distribution. We find that the Logarithmic ACD, if based on a flexible innovation distribution, provides a quite robust and useful framework for the modeling of price and volume duration processes.
We show that multivariate Hawkes processes coupled with the nonparametric estimation procedure first proposed in Bacry and Muzy (2015) can be successfully used to study complex interactions between the time of arrival of orders and their size, observed in a limit order book market. We apply this methodology to high-frequency order book data of futures traded at EUREX. Specifically, we demonstrate how this approach is amenable not only to analyze interplay between different order types (market orders, limit orders, cancellations) but also to include other relevant quantities, such as the order size, into the analysis, showing also that simple models assuming the independence between volume and time are not suitable to describe the data.
●The conditions are officially justified not as punishment for prisoners but as an administrative measure. Prisoners are placed in control units in administrative moves and since there are no rules governing such moves (in contrast to punitive moves), prisoners are denied any due process and prison officials can incarcerate any prisoner in a control unit for as long as they choose, without having to give any reason.