5.2. Standardized foreign exchange returns

The conjectures underlying a components type formulation of the volatility

process are further reinforced by our analysis of the standardized 5-minute returns;

R,. n -Rt.,,/(~-tgt.n). If our model provides a good approximation to the data

generating process, then this series should display little ARCH effects at daily and

lower frequencies, and the intraday ARCH effects should diminish. Consistent

with this prediction, the absolute return autocorrelations at the lowest intraday

frequencies have been reduced markedly. This is also manifest in the lower curves

in Fig. 7a, which depict the correlograms for I/~r.,,L Apart from small spikes

associated with remaining stochastic periodicity at the daily frequency, the correlations

for the absolute returns are generally close to zero beyond the two day lag.

Thus, the daily GARCH(1, 1) volatility estimates appear to provide quite satisfactory

estimates for the interday volatility dynamics 44. At the same time, Fig. 7a is

also indicative of important short-run dynamics that necessarily are unaccounted

for by the daily GARCH(1, 1) volatility estimates. This again lends support to our

conjecture of distinct short-run, or intraday, components in the fundamental return

volatility generating process. The MA(1)-GARCH(1, 1) estimates for the standardized

returns in Table 5a reinforce this interpretation by exhibiting a sharp

decline in &(k) +/3(k) as the return horizon increases from five minutes to one

hour. In fact, beyond the one hour sampling frequency, the volatility clustering is

sufficiently weak that the GARCH(1, l) specification breaks down, and only

ARCH(I) or homoskedastic MA(1) models are estimated.

The conjectures underlying a components type formulation of the volatility

process are further reinforced by our analysis of the standardized 5-minute returns;

R,. n -Rt.,,/(~-tgt.n). If our model provides a good approximation to the data

generating process, then this series should display little ARCH effects at daily and

lower frequencies, and the intraday ARCH effects should diminish. Consistent

with this prediction, the absolute return autocorrelations at the lowest intraday

frequencies have been reduced markedly. This is also manifest in the lower curves

in Fig. 7a, which depict the correlograms for I/~r.,,L Apart from small spikes

associated with remaining stochastic periodicity at the daily frequency, the correlations

for the absolute returns are generally close to zero beyond the two day lag.

Thus, the daily GARCH(1, 1) volatility estimates appear to provide quite satisfactory

estimates for the interday volatility dynamics 44. At the same time, Fig. 7a is

also indicative of important short-run dynamics that necessarily are unaccounted

for by the daily GARCH(1, 1) volatility estimates. This again lends support to our

conjecture of distinct short-run, or intraday, components in the fundamental return

volatility generating process. The MA(1)-GARCH(1, 1) estimates for the standardized

returns in Table 5a reinforce this interpretation by exhibiting a sharp

decline in &(k) +/3(k) as the return horizon increases from five minutes to one

hour. In fact, beyond the one hour sampling frequency, the volatility clustering is

sufficiently weak that the GARCH(1, l) specification breaks down, and only

ARCH(I) or homoskedastic MA(1) models are estimated.