The intensity of trading activities can be measured in a number of ways. The most common measure in use is volume, which is simply the number of shares traded during a certain time interval. Given that the liquidity (which shows how easy it is to trade an asset) and therefore the absolute trading activity in each stock is different, the volume expressed in percentage form is a more convenient choice for modeling purposes. This measure is called turnover, which is formally computed from volume, as follows:
Here, x stands for turnover, V for volume, and TSO for the total shares outstanding; the latter indicates the total number of shares available for public trading. The index i indicates the actual stock, and index t indicates the time interval.
As mentioned earlier, there are several stylized facts documented in volume. An obvious one is that volume is non-negative, given that it measures the number of traded shares. This number is zero, if there are no trades at all, and positive otherwise. Another important stylized fact is the intra-daily U shape registered on several different markets (see Hmaied, D. M., Sioud, O. B., and Grar, A. (2006) and Hussain, S. M. (2011) for a good overview).
This means that the trading activity tends to be more intense after opening and before closure of the market, than during the rest of the day. There are several possible explanations for this phenomenon, but its existence is very clear.
Note
The enthusiastic reader might be interested in Kaastra, I. and Boyd, M. S. (1995) and Lux, T. and Kaizoji, T. (2004), which propose volume-forecasting models using monthly and daily data respectively. Brownlees, C. T., Cipollini, F., and Gallo, G. M. (2011) builds a volume forecasting model for intra-day data, which is of direct relevance to this chapter. Our empirical investigations found that the model detailed in the following section (proposed by Bialkowski, J., Darolles, S., and Le Fol, G. (2008)) provides a more precise forecast, so merely due to length limitations, this chapter only elaborates on the latter.
This chapter addresses the intra-day forecasting of stock volumes. There are a few models that can be found in the literature, among which we found that the one presented in Bialkowski, J., Darolles, S., and Le Fol, G. (2008) is the most accurate. The following section briefly summarizes the model, providing enough detail to understand the implementation later on.