In recent years, more forecasting success is being reported from the use of innovative
econometric methods, such as switching models, factor models and better forecast test
statistics. For example, Nikolsko-Rzhevskyy and Prodan (2012) suggest modelling the
exchange rate as a 2-state Markov switching random walk with drift and demonstrate
that this model strongly outperforms the random walk at both short and long horizons.
There is also a growing literature on using factor analysis in modelling exchange
rates. For example, Engel, Mark and West (2012) construct I(1) factors from a cross
3section of 17 quarterly exchange rates and use the idiosyncratic deviations from the
factors for forecasting. They demonstrate that forecasts using factors, and using factors
combined with PPP fundamentals improve on random walk benchmark for the
sample 1999–2007. Greenaway-McGrevy, Mark, Sul and Wu (2012) apply a similar
methodology to a panel of 23 monthly bilateral exchange rates with the U.S. dollar for
the period January 1999 to December 2010. They identify counterparts of the three
factors to be euro/dollar, yen/dollar and swiss frank/dollar exchange rate. The authors
demonstrate that the exchange rate model incorporating factors has a significant
predictive power. Like many other recent papers, these two studies focus on improved
asymptotic forecasting tests, in particular the Clark-West test, to assist in the success
of their estimation models in defeating the random walk.
Our approach extracts common components in the movements of bilateral exchange
rates, utilizing the principal components for forecasting. We also call them ‘factors’
although the PCA method is different from factor analysis in several aspects. In particular,
there is an explicit model in factor analysis for unobservable factors and their
relationship with the variables of interest. Also, the principal components in PCA are
orthogonal to each other while the factors in factor models need not be. We do not
use I(1) factors as Engel et al. (2012) and Greenaway-McGrevy et al. (2012). Instead,
we are interested in principal component analysis and since it can only be applied generally
to stationary (or non-integrated) time series, we consider percentage changes of
the exchange rates. In this respect our approach is similar to Lustig, Roussanov and
Verdelhan (2011) who also consider changes in exchange rates and identify a global
risk factor driving these changes. However, their focus is more on asset pricing and
they are not directly interested in forecasting.
One advantage of using principal component analysis is that we concentrate on a
subset of the estimated factors, which are the most important for explaining the cross-
4sectional variance in the percentage changes of exchange rates. However, this approach
has a disadvantage: the constructed factors do not always have obvious interpretations.
Using fifteen monthly percentage changes in bilateral exchange rates against the U.S.
dollar since 1999, the purpose of this paper is to identify the most important estimated
factor (or component) that drives changes in all the bilateral U.S. exchange rates.
Given the commonality of the U.S. in this dataset of bilateral exchange rates, we conjecture
that this factor is closely related to U.S. fundamentals, including both nominal
and real macroeconomic variables, and financial market variables. The dominance of
the U.S. for this factor is also recommended because it is the world’s major economy
and its safe haven in times of uncertainty. We find this conjecture is supported, and
further that other countries, however large, play no statistical part. Using the information
yielded by this factor alone, we find that we can forecast the levels of bilateral
exchange rates significantly better than the random walk (using the Clark-West test)
for almost all currencies considered in the sample. In addition to monthly data we also
consider weekly and daily data. We find that the first principal component is useful
for forecasting at a weekly frequency but cannot beat the random walk for daily data.
The rest of the paper is organised as follows. Section 2 performs the principal component
analysis, identifies the main factor and links it to the U.S. macro and financial
variables. Section 3 discusses the relationship between the first principal component
and the fundamentals across the time. Section 4 presents the results of exchange rate
forecasting using monthly data. Section 5 focuses on exchange rate forecasting using
weekly and daily frequencies. Section 6 concludes.