Page 347 - Special Topic Session (STS) - Volume 3

STS550 Pierre Guérin et al.
currencies. We extract factors from the MS-3PRF, MSS-3PRF, linear 3PRF,
PCA, TPCA and PC-LARS. We then use the resulting factors to forecast
selected bilateral exchange rates. (All currency pairs use the USD as
numéraire.) The choice of the data set draws from the exercise in
Greenaway-McGrevy et al. (2016). The data set is monthly, and the full
sample size extends from January 1995 to December 2015. The data are
obtained from the International Financial Statistics of the International
Monetary Fund, and the monthly data are taken as the monthly average of
daily data. The data set consists of the currencies of Australia (AUS),Brazil
(BRA), Canada (CAN), Chile (CHI), Columbia (COL), the Czech Republic (CZE),
the euro (EUR), Hungary (HUN), Iceland (ICE), India (IND), Israel (ISR), Japan
(JPN), Korea (KOR), Mexico (MEX), Norway (NOR), New Zealand (NZE), the
Philippines (PHI), Poland (POL), Romania (ROM), Singapore (SIN), South
Africa (RSA), Sweden (SWE), Switzerland (SUI), Taiwan (TAI), Turkey (TUR)
and the United Kingdom (GBR).
The left-hand side of Table 1 reports point forecasting results for
specific currencies: the Canadian dollar (CAD), the euro (EUR), the Japanese
yen (JPY) and the British pound (GBP), all relative to the USD. These are G7
currencies, and among the most traded currency pairs according to the
Bank for International Settlements Triennial Central Bank Survey. The point
forecast results are presented as the MSFE of a specific approach relative
to the MSFE obtained from the no-change forecast. The no-change forecast
is the standard benchmark in the exchange rate forecasting literature (see,
e.g., Rossi (2013)). We also report the results of the Diebold and Mariano
(1995) test of equal out-of-sample predictive accuracy using the no-change
forecast as a benchmark. First, the models’ forecasting performance relative
to the no-change forecast is typically the strongest for forecast horizon ℎ =
1 (except for the JPY/USD). The improvement in forecast accuracy relative
to the random walk is also statistically significant according to the Diebold
and Mariano test of equal MSFE when forecasting the Canadian dollar at
forecast horizon ℎ = 1 across most approaches (this is also true to a lesser
extent for the British pound). Second, the PC-LARS approach performs best
for forecast horizon ℎ = 1 when forecasting the British pound. Moreover,
the MS-3PRF (first and third pass) approach performs best when
forecasting the Canadian dollar for forecast horizons ℎ > 1. Third, for the
Canadian dollar and the Japanese yen, modelling time variation in the
forecasting equation is relevant in that this leads to substantial forecasting
improvement over the no-change forecast at distant forecast horizons ℎ =
{9} for the Japanese yen and ℎ = {2, 3, 6, 9, 12} using the MS-3PRF (first and
third passes) approach.
Next, the right-hand side of Table 1 shows the directional accuracy
forecasting results, which are broadly in line with the point forecast

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