Analysis of Financial Time Series, Third Edition

5.3 Empirical Characteristics of Transactions Data

Let ti be the calendar time, measured in seconds from midnight, at which the ith transaction of an asset takes place. Associated with the transaction are several variables such as the transaction price, the transaction volume, the prevailing bid and ask quotes, and so on. The collection of ti and the associated measurements are referred to as the transactions data. These data have several important characteristics that do not exist when the observations are aggregated over time. Some of the characteristics are given next.

1. Unequally Spaced Time Intervals Transactions such as stock tradings on an exchange do not occur at equally spaced time intervals. As such, the observed transaction prices of an asset do not form an equally spaced time series. The time duration between trades becomes important and might contain useful information about market microstructure (e.g., trading intensity).

2. Discrete-Valued Prices The price change of an asset from one transaction to the next only occurred in multiples of tick size before January 29, 2001. On the NYSE, the tick size was one-eighth of a dollar before June 24, 1997 and was one-sixteenth of a dollar before January 29, 2001. Therefore, the price was a discrete-valued variable in transactions data. Although all equity markets in the United States now use the decimal system, the price change in consecutive trades tends to occur in multiples of one cent and can be treated approximately ...