Ruey S. Tsay 1015LagACF01 02 03 04 00.00.20.40.6(a) Sample ACF of the daily range of log priceLagACF–0.2 –0.1 0.0 0.1 0.2 01 02 03 04 0(b) Sample ACF of standardized residuals of a GACD(1,1) modelFigure 21.5 The sample autocorrelation function of the daily range of log price of Apple
stock from January 4, 1999 to November 20, 2007: (a) ACF of daily range; (b) ACF of the
standardized residual series of a GACD(1,1) model
of volatility clustering, for a large volatility tends to be followed by another large
volatility. This phenomenon is different from that of the transaction durations in
Example 1 for whichαˆis less than 1.
21.4 The diurnal pattern
In this section, we discuss a simple method to adjust the diurnal pattern of
intradaily trading activities. Figure 21.7(a) shows the trade durations of General
Motors (GM) stock from December 1 to December 5, 2003. Again, for simplicity,
zero durations are ignored. Figure 21.7(b) shows the time intervals from the market
opening (9.30 a.m. Eastern time) to the transaction time. The four vertical drops
of the intervals signify the five trading days. From parts (a) and (b) of the figure,
the diurnal pattern of trading activities is clearly seen. Specifically, except for a
few outliers, the trade durations exhibit a cap-shape pattern within a trading day,
namely the durations are in general shorter at the beginning and closing of the
market, and longer around the middle of a trading day. One must consider such a
diurnal pattern in modeling the transaction durations.