obvious from Figs. 1, 3, 5, 7 and 9, the fourth row of Table 2 shows the percentage increases in the mean coherence between the two periods. These percentage
increases are 21 USHong Kong, 7 USAustralia, 32 CanadaJapan, and 15 CanadaHong Kong. The CanadaAustralian coherence combination is the
only statistic which indicates a shift to a lower mean coherence in the post-crash period. These statistics are consistent with the results of the Wilcoxon Z statistics.
The phase statistics for the North American markets relative to the Western Pacific region consistently show alternating significant leads of the North American
market over the Western Pacific markets at high frequencies, with the lead falling at longer frequencies. Beyond a frequency of 0.2 5 days there is very little
difference between the pre-and post-crash phase leads. This is in contrast to the phase relationships among the Western Pacific markets discussed below.
5. Results for western pacific region
The pre- and post-crash coherences for the Japanese and Hong Kong indexes are shown in Fig. 11. The post-crash peak, mean, and median coherences are greater
than pre-crash coherences. Additionally, the Wilcoxon Z statistic − 17.2 strongly rejects the null that the pre- and post-crash coherences are drawn from the same
population. The visual evidence is not so convincing. The post-crash coherence is greater at low frequencies 0.5 – 0.4, lower at intermediate frequencies 0.4 – 0.3,
and again higher at lower frequencies beyond about 0.3. However, the statistical analysis strongly suggests that the post-crash coherences are greater.
The JapaneseHong Kong phase lead is plotted in Fig. 12. Initially, at high frequencies the Hong Kong market leads the Japanese market. At about a
frequency of 0.38 3 days the Japanese market begins to lead, with several ‘switches’ beyond a frequency of 0.2 5 days. This pattern is consistent across both
periods. It is noteworthy that these leads, whether Japanese or Hong Kong, are
Fig. 11. Coherence between Japanese and Hong Kong indexes: pre- vs. post-crash.
Fig. 12. Phase between Japanese and Hong Kong stock indexes: pre- vs. post-crash.
Fig. 13. Coherence between Japanese and Australian indexes: pre- vs. post-crash.
short. At a frequency 0.3 about 3 days the pre-crash lead peaks at only 1 radian. The largest lead of the Hong Kong market is in the pre-crash period at a frequency
of 0.4 2.5 days. Coherence between the Japanese and Australian markets are displayed in Fig. 13.
Visually, there appears to not be much to distinguish the low pre- and post-crash coherences, particularly at frequencies beyond 0.2 5 days. However, both the
post-crash mean and median are greater. The Wilcoxon Z statistic from Table 2 indicates differing populations. The pre-crash coherence is not statistically signifi-
cant at about a frequency of about 0.3.
3
3
The statistical significance of the coherences is testing using the F test, 2mw ˆ
ij
vr
2
1 − w ˆ
ij
vr
2
with 2,4m m is the window width degrees of freedom see Priestley, 1981, p. 706. With a window width of 150 days, the critical F
0.01
and F
0.05
values are 4.61 and 3.00, respectively.
Fig. 14 shows the phase lead between the Japanese and Australian markets. At high frequencies, there is a dramatic difference between the two periods. In the
post-crash period the lead of the Japanese market is greatly reduced. Indeed, at very high frequencies the Australian market leads. The spike in the pre-crash phase
lead at about a frequency of 0.3 is due to the lack of statistical significance in the pre-crash coherence noted above.
Fig. 15 plots the coherences between the Australian and Hong Kong indexes. The pattern is similar in that the coherences, for both periods, are low at high
frequencies, rising at lower frequencies. There is something unique to this pairwise comparison of the two markets. From Table 2, the Wilcoxon Z statistic cannot
reject that the coherences are drawn from different populations. This is the only pairwise comparison where this is true. These data clearly indicate that the pre- and
post-crash coherences are statistically indistinguishable.
Fig. 14. Phase between Japanese and Australian stock indexes: pre- vs. post-crash.
Fig. 15. Coherence between Australian and Hong Kong indexes: pre- vs. post-crash.
Fig. 16. Phase between Australian and Hong Kong stock indexes: pre- vs. post-crash.
The phase lead for these markets is shown in Fig. 16. The leads are short, with the Hong Kong market leading at most frequencies. The Hong Kong market leads
by no more than 1 radian at a pre-crash frequency of about 0.35. The coherences among the Western Pacific markets are not as great as those that
include the North American markets. From Table 2, the pre-crash peak coherences for these markets range from 0.2415 JapanHong Kong to 0.5818 CanadaAus-
tralia. However, the mean coherences of these markets rise in the post-crash period by 40 JapanHong Kong, 15 JapanAustralia and 6 AustraliaHong Kong.
Again, these results are consistent with the Wilcoxon Z statistics, indicating a significant upward shift in the distribution of coherences from the pre- to post-crash
period.
The phase diagrams show a somewhat mixed pattern for the Western Pacific pairwise combinations. First, in contrast to the North AmericanWestern Pacific
markets, the leads vary between the input and the output markets. Second, consistent with the previous results, the pre-crash high frequency phase lead of the
Japanese market over the Australian market is similar to that of the North AmericanWestern Pacific results. However, this phase lead is reduced in the
post-crash period, indicating greater synchronization of the two markets. In con- trast, the patterns for the JapaneseHong Kong and AustralianHong Kong mar-
kets are quite similar in that their market cycles exhibit smaller leadslags in phase in both the pre- and post-crash periods. It is likely that there is greater synchroniza-
tion of leads with these markets being concentrated geographically. This also could explain the leads at high frequencies of the North American markets over the
Western Pacific markets.
6. Conclusions and implications
