Equity Valuation and Portfolio Management

HIGH-FREQUENCY DATA ARE IRREGULARLY SPACED IN TIME

Most modern computational techniques have been developed to work with regularly spaced data, presented in monthly, weekly, daily, hourly, or other consistent intervals. The traditional reliance of researchers on fixed time intervals is due to:

• Relative availability of daily data (newspapers have published daily quotes since the 1920s).
• Relative ease of processing regularly spaced data.
• An outdated view, as noted by Goodhart and O'Hara⁶ that “whatever drove security prices and returns, it probably did not vary significantly over short time intervals.”

In contrast, high-frequency observations are separated by varying time intervals. One way to overcome the irregularities in the data are to sample it at certain predetermined periods of time—for example, every hour or minute. For example, if the data is to be converted from tick data to minute “bars,” then under the traditional approach, the bid or ask price for any given minute would be determined as the last quote that arrived during that particular minute. If no quotes arrived during a certain minute, then the previous minute's last tick would be taken as the current minute's quote, and so on. Exhibit 20.7(A) illustrates this idea. This approach implicitly assumes that in the absence of new quotes, the prices stay constant, which does not have to be the case.

Dacorogna, Gencay, Muller, Olsen, and Pictet propose a potentially more precise way to sample quotes—linear time-weighted ...