Advances in Risk Management

230 CORRELATION BREAKDOWNS IN ASSET MANAGEMENT

1.5

100 200 300 400 500

1.0

0.5

0.0

1.0

0.5

RESID Number of observations  558 daily changes

Spread between actual and estimated

dependent variable

No. of observations

Figure 12.4Plot of residuals of correlation EUR–USD changes explained

by volatility differences

in Table 12.2. In particular, only a variable of the Euro market is statistically
significant (3 days lag), while the US market explains the dependent vari-
able with three variables (1–3 and 8 days lag). But, what is clearly higher is
theR-squared value which reaches a level around 50 percent. In this case,
the Durbin–Watson statistic shows a value of 2.26, which should be a little
negative correlation. Actually, there are some limitations of the DW test as
a test for serial correlation. One of them is the fact that if there are lagged
dependent variables on the right-hand side of the regression equation the
DW test is no longer valid.^2
Consistent with the higherR-squared value, residuals are graduated
within a range of (−0.35; 0.42) while the equation estimated over the com-
plete time series has a range of (−0.55; 1.19). In Figure 12.5 the Euro–US
market correlation residuals are reported. Table 12.3 proves that the correla-
tion delta between the Euro area market and the Japanese market cannot be
as well explained as the Euro area market versus the US market. In particu-
lar, theR-squared index is about 5.5 percent. The sum of squared residuals
of the Euro–Japan market is 181.68.
Figure 12.6 demonstrates that the range of residuals is (−1.87; 9.53). In
this case, the residuals of the higher correlations (Figure 12.7). Move within
a range which is very similar in the negative side (−1.93) but lower in the
positive side (8.11).
Even though theR-squared value is lower, the value of the higher cor-
relation changes is 11 percent. In this case only two explicative variables
enter the equation, respectively the variation of the volatility measured in