involved when employing estimated explanatory variables.27 For the latter reasons we will
use GARCH based volatility measures to approximate FX uncertainty.
A preliminary view at the first differences of most country specific effective real FX rates,
∆ekt = ekt - ekt-1 , revealed marked patterns of volatility clustering, and at the same time a
few processes showed one or two outlying observations. For some countries initial volatility
estimates obtained when modelling ∆ekt directly turned out to give unsatisfactorily diagnos-
tic features of standardized residuals or implausible signs of coefficient estimates. Therefore
we decided to apply a trimming procedure replacing realizations of ∆ekt which exceed in
absolute value 2.5 times their empirical standard deviation (σe), by ±2.5σe preserving the
initial sign of ∆ekt .
Conditional FX volatility time paths of the real effective FX uncertainty are (mostly)
estimated by means of GARCH(1,1) models, i.e.
∆ekt
2
vkt
ʌ
ξktVkt, ξkt ~ N(0,1),
^ko + ^ki(∆ekt-ι)2 + ∕^kivkt-ι∙
(3)
(4)
Recall that the notation does not discriminate the cases of exports and imports. The
GARCH(1,1) process as specified in (3) and (4) postulates a normal distribution for ∆ekt the
variance of which is conditional on Ωt-1. Positive estimates of the parameters in equation
(3) (δk0 > 0, δ∣k1 > 0,βk1 > 0) are sufficient for positivity of the conditional variances v2t.
Covariance stationarity of the GARCH process (∆ekt)2 requires δk1 + ∕k1 < 1. Since the
GARCH model is a univariate specification the conditional variance estimates will also have
to catch up other potential sources of time varying volatility. Opposite to other measures of
exchange rate volatility, however, the analyst may augment (4) with exogenous variables if
indicated by diagnostic tests.
insert Table III about here
2.2.3 Volatility estimates
Diagnostic tests and GARCH(1,1) parameter estimates are provided in Table III. Parameter
estimates are fairly similar between the models estimated for exports and imports indicating
that weights attached to partner countries remain similar when analyzing exports or im-
ports (see also Table II). According to one sided significance tests two third of all empirical
models show significant parameter estimates δ>k1 or βk1 at the 5% level. This underscores
the existence of volatility clustering in monthly real effective FX rates. Due to sluggish
and lagged adjustment practice of trading agents the current impact of volatility may have
only minor importance for current growth rates of trade flows. However, given sufficiently
smooth volatility paths current volatility is a meaningful approximation of FX uncertainty
taken into account by traders. For those countries where both coefficient estimates δ>k1 and
βk1 were insignificant (or negative) we also tried an ARCH(I) specification. Owing to better