The logarithmic vector multiplicative error model: an application to high frequency NYSE stock data

Abstract

We develop a general form logarithmic vector multiplicative error model (log-vMEM). The log-vMEM improves on existing models in two ways. First, it is a more general form model as it allows the error terms to be cross-dependent and relaxes weak exogeneity restrictions. Second, the log-vMEM specification guarantees that the conditional means are non-negative without any restrictions imposed on the parameters. We further propose a multivariate lognormal distribution and a joint maximum likelihood estimation strategy. The model is applied to high frequency data associated with a number of NYSE-listed stocks. The results reveal empirical support for full interdependence of trading duration, volume and volatility, with the log-vMEM providing a better fit to the data than a competing model. Moreover, we find that unexpected duration and volume dominate observed duration and volume in terms of information content, and that volatility and volatility shocks affect duration in different directions. These results are interpreted with reference to extant microstructure theory.