3.1. Intraday return correlations

While the intraday volatility patterns documented in the preceding section may

be irrelevant for standard studies of the return dynamics based on price observations at daily frequencies, conclusions drawn from the recent surge of empirical

papers on return volatility and market microstructure variables at the intraday

frequencies are likely subject to severe distortions due to the strong periodicity in

returns. We therefore supplement the prior investigation of the unconditional

volatility patterns with an explicit look at the dynamic features of our two return

series.

Fig. 3a and b display the sample autocorrelations of the 5-minute returns for up

to five days i.e. 1440 observations for the foreign exchange and 400 for the equity

returns. All values are small and beyond the first few lags the series resemble

realizations of white noise. Thus, we again detect little of interest in the mean

Five Days Correlogram

0.02

0.01

0.00

-0.01

o -0,02

-0.03 1-

-0.04 (a)

0 250 500 750 ~ 000 1250 1500

Five Minute Lag

Five Days Correlogram

tJlJ ..... , lliLii l,i ti,iil, iii 0.00 I ,

--0.01

(b)

- 0 . 0 2 , , ' , ' , ' ' ' ' 0 5'0 100 150 2;0 2;0 3;0 3;0 400

Five Minute Lag

Fig. 3. Five days correlogram of intraday returns, (a) DM-$, (b) S&P 500.

T. G. Andersen, T. Bollerslev / Journal of Empirical Finance 4 (1997) 115-158 125

returns. In contrast, the autocorrelation patterns for the absolute returns are

strikingly regular. Consider the series for the DM-$ exchange rate in Fig. 4a. The

strong intraday pattern induces a distorted U-shape in the sample correlogram ~9

Notice also how the size of the autocorrelations at the daily frequencies decay

slowly over the first four days, only to increase slightly at the fifth, or weekly,

frequency. This signals the presence of a minor day-of-the-week effect, which we

ignore in the remainder. Fig. 4b for the S &P 500 futures returns is equally telling.

The slowly declining U-shape occupies exactly 80 intervals, corresponding to the

daily frequency.

While the intraday volatility patterns documented in the preceding section may

be irrelevant for standard studies of the return dynamics based on price observations at daily frequencies, conclusions drawn from the recent surge of empirical

papers on return volatility and market microstructure variables at the intraday

frequencies are likely subject to severe distortions due to the strong periodicity in

returns. We therefore supplement the prior investigation of the unconditional

volatility patterns with an explicit look at the dynamic features of our two return

series.

Fig. 3a and b display the sample autocorrelations of the 5-minute returns for up

to five days i.e. 1440 observations for the foreign exchange and 400 for the equity

returns. All values are small and beyond the first few lags the series resemble

realizations of white noise. Thus, we again detect little of interest in the mean

Five Days Correlogram

0.02

0.01

0.00

-0.01

o -0,02

-0.03 1-

-0.04 (a)

0 250 500 750 ~ 000 1250 1500

Five Minute Lag

Five Days Correlogram

tJlJ ..... , lliLii l,i ti,iil, iii 0.00 I ,

--0.01

(b)

- 0 . 0 2 , , ' , ' , ' ' ' ' 0 5'0 100 150 2;0 2;0 3;0 3;0 400

Five Minute Lag

Fig. 3. Five days correlogram of intraday returns, (a) DM-$, (b) S&P 500.

T. G. Andersen, T. Bollerslev / Journal of Empirical Finance 4 (1997) 115-158 125

returns. In contrast, the autocorrelation patterns for the absolute returns are

strikingly regular. Consider the series for the DM-$ exchange rate in Fig. 4a. The

strong intraday pattern induces a distorted U-shape in the sample correlogram ~9

Notice also how the size of the autocorrelations at the daily frequencies decay

slowly over the first four days, only to increase slightly at the fifth, or weekly,

frequency. This signals the presence of a minor day-of-the-week effect, which we

ignore in the remainder. Fig. 4b for the S &P 500 futures returns is equally telling.

The slowly declining U-shape occupies exactly 80 intervals, corresponding to the

daily frequency.