Price duration versus trading volume in high-frequency data for selected DAX companies

The main goal of this paper is to gain insights into the dependence structure between the duration and trading volume of selected stocks listed on the Frankfurt Stock Exchange. We demonstrate the usefulness of the copula function to describe the dependence of specific unevenly spaced time series. The properties of the time series of price durations and trading volumes under study are in line with common observations from other empirical studies. We observe clustering, overdispersion, and diurnality. For most of the stocks, the seminal model (linear parametrization with exponential or Weibull distribution) can be replaced by a logarithmic specification with more-flexible conditional distributions. The price duration and trading volume associated with this duration exhibit dependence in the tails of distribution. We may conclude that high cumulative trading volumes are associated with long duration. However, changes of price over short times are related to low cumulative volume.