In this paper, we studied the dependence structure of exchange rate pairs in the form of correlation
and tail dependence. The correlation gives information about how two currencies move
together “on average” across the distribution. However, the correlation imposes symmetry in
the way exchange rates co-move in the two tails of the distribution. With the view that this
might be too big of a restriction when analyzing exchange rates, and following Patton (2006b),
we studied the dependence/co-movement between exchange rate pairs also in the form of upper
and lower tail dependence. Moreover, we analyzed the evolution of the correlation, upper
and lower tail dependence parameters over time, and investigated whether these parameters are
affected by business cycles and interest rate differentials.
Our results show that:
(i) In the constant copula models, the difference between the upper and the lower tail parameters
tends to be negative (when significant) in the plain model and in the models with
recessions, except when the yen is involved. A negative difference between the upper and the
lower tail parameters means that the U.S. dollar is more likely to depreciate than appreciate
jointly against the other currencies.
(ii) In the time-varying models, the dependence parameters fluctuate heavily over time and
are well outside the 95 percent confidence bands of the constant estimates.
(iii) In the foreign recession model, in many cases when significant, a recession in a country
tends to increase the dependence (correlation, upper and lower tail) between currency pairs.
Notable exceptions are Japanese recessions, which tend to de-couple the yen from the othercurrencies.
(iv) The U.S. business cycle never affects the time variation in the upper tail dependence
between currency pairs, but it increases the lower tail dependence for 5 out of 14 currency pairs,
meaning that if there is a recession in the United States, some currencies are more likely to
experience a joint steep appreciation against the dollar than during other periods.
(v) When significant, the effects of a higher interest rate differential are almost always negative,
meaning that currencies with higher interest rate differentials tend to move less closely
together, not only on average (correlation), but also when extreme events occur (tails). In the
ten-year rate models, the upper tail dependence is much more frequently affected significantly
by the interest rate differentials than the lower tail.