Joe Cardinale and Larry W. Taylor 329̂I=1, and there isperfect negative synchronizationif̂I=0. Beyond the literature
on national output, Edwards, Biscarri and de Gracia (2003) observe that financial
synchronization, orconcordance, among Latin American countries has substantially
increased after financial liberalization.7.7.2 Correlation analysis
The sample correlation coefficient betweenS 1 andS 2 , call itrs, conveys similar
information tôI.Ifrs=1, there is evidence in favor of the null hypothesis,H 0 :
ρs=1, sinceS 1 t=S 2 tfor every paired observation in the sample. Of course, if there
is a single case whereS 1 t =S 2 t, there is reason to reject the hypothesis that the
cycles areperfectlypositively synchronized. Similar reasoning holds true for perfect
negative synchronization. A formal test ofH 0 :ρs=1 is presented by Harding and
Pagan (2006).
As perfect synchronization will be empirically atypical, it is still useful to compute
either or both of the sample correlation coefficient and coincidence indicator to
see how closely two series move in tandem. Graphing the series may also reveal an
obvious translation of{S 1 t}that will more closely synchronize{S 1 t}with{S 2 t}. For
instance, consider{S 3 t}={S1,t±l}for some integerl>0. The concordance between
{S 3 t}and{S 2 t}may be considerably higher than the concordance between{S 1 t}and
{S 2 t}if lagged effects are important. Alternatively, it may be that changing just a
few turning points could lead to near-perfect concordance between two series. If
so, sensitivity analysis is worthwhile.7.7.2.1 Tests based on the method of moments
It is important to formally test for no synchronizationH 0 :ρs=0, since this
implies that{S 1 t}and{S 2 t}are unrelated series with no common cycle. As a case in
point, the business cycles of the United States and the United Kingdom could have
high concordance simply because most of the time these economies are expanding,
not contracting. On the other hand, whether these two economies actuallymove
togetheris a different issue. In other words, although{S 1 t}and{S 2 t}may be highly
synchronized, this does not by itself imply a common cycle.
Under classical conditions, several tests forH 0 :ρs= 0 are equivalent. For
instance, we can employ:tr=rs√
T− 2
1 −rs^2a N(0, 1). (7.22)Numerically equivalent test statistics are the standardt-ratios for the slope coeffi-
cients in eitherS 1 t=α+βS 2 t+ε 1 torS 2 t=γ+δS 1 t+ε 2 t. However, the situation
is complicated by the fact thatS 1 is serially correlated, as isS 2 , and thus the inde-
pendence assumption associated with the traditionalt-test of zero-correlation is
compromised. Therefore, the statistic used to testH 0 :ρs=0 must be made robust
to serial correlation and heteroskedasticity.^14 Harding and Pagan (2006) recom-
mend that the test statistic be constructed via GMM with a robust variance estimate
to account for serial correlation and heteroskedasticity.