5.4. Standardized equity returns

In contrast to the results for the DM-$, the first order autocorrelations for the

standardized absolute returns for the S&P 500, [R^tk,, ,I, remain highly significant for

I the lower intraday frequencies, Even at the ?- day return frequency, pA = 0.094

exceed the corresponding asymptotic standard error by more than a factor four.

This is also confirmed by the much higher a(k ) +/3(k ) estimates for the intraday

GARCH(1, 1) models for /~ given in Table 5b. Similarly, the correlograms in 1,7l

Fig. 7b for the standardized returns indicate a much higher degree of volatility

persistence in the 5-minute S &P 500 returns than was the case for DM-$ returns.

In fact, the standardized absolute return correlogram stays mostly positive for the

first 22 trading days, or about a month. This indication of more persistent volatility

dynamics is likely attributable to the longer time span for the equity data. For

example, Dacorogna et al. (1993) find that the absolute standardized return

autocorrelations remain positive for one month when using 20-minute DM-$ data

over a four year sample. Additionally, from Guillaume (1994) it is evident that our

ability to detect significant long-horizon absolute return correlations is intimately

linked to the length of the sampling period. Hence, although the interdaily

GARCH(1, 1) model may capture a large portion of the day-to-day volatility

clustering, the model's deficiency in dealing with long-memory behavior necessarily

becomes more transparent when the time span of the data increases.

We conclude, that in spite of important institutional differences in the markets

and the associated intradaily volatility patterns, there is strong indications that the

volatility processes for the foreign exchange and the U.S. equity market share

several important qualitative dynamic features. Moreover, these characteristics

were largely invisible prior to our filtration of the intraday periodic structures in

the high frequency return series. At the same time interesting differences between

the average volatility level and volatility persistence in the two markets also

emerge. These conclusions would be next to impossible to reach from the, at first

sight, rather perplexing estimates obtained directly from the raw high frequency

returns.

In contrast to the results for the DM-$, the first order autocorrelations for the

standardized absolute returns for the S&P 500, [R^tk,, ,I, remain highly significant for

I the lower intraday frequencies, Even at the ?- day return frequency, pA = 0.094

exceed the corresponding asymptotic standard error by more than a factor four.

This is also confirmed by the much higher a(k ) +/3(k ) estimates for the intraday

GARCH(1, 1) models for /~ given in Table 5b. Similarly, the correlograms in 1,7l

Fig. 7b for the standardized returns indicate a much higher degree of volatility

persistence in the 5-minute S &P 500 returns than was the case for DM-$ returns.

In fact, the standardized absolute return correlogram stays mostly positive for the

first 22 trading days, or about a month. This indication of more persistent volatility

dynamics is likely attributable to the longer time span for the equity data. For

example, Dacorogna et al. (1993) find that the absolute standardized return

autocorrelations remain positive for one month when using 20-minute DM-$ data

over a four year sample. Additionally, from Guillaume (1994) it is evident that our

ability to detect significant long-horizon absolute return correlations is intimately

linked to the length of the sampling period. Hence, although the interdaily

GARCH(1, 1) model may capture a large portion of the day-to-day volatility

clustering, the model's deficiency in dealing with long-memory behavior necessarily

becomes more transparent when the time span of the data increases.

We conclude, that in spite of important institutional differences in the markets

and the associated intradaily volatility patterns, there is strong indications that the

volatility processes for the foreign exchange and the U.S. equity market share

several important qualitative dynamic features. Moreover, these characteristics

were largely invisible prior to our filtration of the intraday periodic structures in

the high frequency return series. At the same time interesting differences between

the average volatility level and volatility persistence in the two markets also

emerge. These conclusions would be next to impossible to reach from the, at first

sight, rather perplexing estimates obtained directly from the raw high frequency

returns.