What is a Good Information Proxy?

Abstract

This article compares the qualities of several intraday activity measures as information proxy. These information proxies are: - the number of trades; - the volume of trades, - the number of incoming orders; - the volume of incomings orders. Relying on the MDH hypothesis, a good information proxy should induce a reduction of the well known deviations from the Markov-Gaussian hypothesis. Although, this approach has rarely been used at an intraday level. This articles uses several time deformations: the time is not measured in number of minutes and seconds but according to a measure of the activity. All the time deformations respect the daily structure of the data: we only distort the time measurement between the first and the last trade on each day. We then analyze the returns properties in these time measurements. The distance between the empirical facts we observe and the theoretical properties we expect enables us to rank the activity measures.

Two different ways are used to compare the activity measures. First, we evaluate the reduction of the well known intraday patterns. Second, we compare the statistical properties of the returns. The conclusion of these two criteria are broadly consistent: None of the activity measure satisfy the validation criteria (disappearance of the intraday pattern and normality of the returns). Although, this study leads to several interesting conclusions. First, activity measures from the trades are better than from those from the incomings orders. Second, a number of events is preferable to a volume of events. Hence, the ranking among the four activity measures is: the number of trades, the volume of trades, the number of orders introduced, the volume of orders.

This study also underlines that the results are influenced by the interval length. For instance, according to the length, the volume may or may not have an information content beyond the number of trades. This fact suggests that a better understanding of the micro-phenomena (trade-by-trade study) is required to get a firm conclusion about the informational relationships at an intraday level.