Advances in Risk Management

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RESID

Number of observations  56 daily changes

Spread between actual and estimated

dependent variable

No. of observations

Figure 12.9 Plot of residuals of correlation USD–JPY higher changes

explained by volatility differences

Table 12.8 Improvement of statistical tests applied to correlation jumps

EUR/USD EUR/JPY USD/JPY

Sum squared residuals 81.50% 43.91% 29.71%
R-squared 63.95% 50.11% 95.32%

Notes:R-squared is the statistical measure of the success of the regression in predicting the values of
the dependent variable within the sample. This measure is the fraction of the variance of the depen-
dent variable explained by the independent variables. The statistic will equal one if the regression fits
perfectly, and zero if it fits no better than the simple mean of the dependent variable. All these values
are obtained as the complement to 1 of the ratio between the test of the complete time series and
the same test of the higher correlations.

Table 12.9 Out of sample model efficiency: mean absolute error

All the correlations

MAE EUR/USD EUR/JPY USD/JPY

11.38% 35.05% 66.41%

Correlations higher changes

MAE EUR/USD EUR/JPY USD/JPY

8.47% 29.61% 47.15%

Note: MAE=mean absolute error.