Palgrave Handbook of Econometrics: Applied Econometrics

1056 The Econometrics of Exchange Rates

4. Repeat steps 2 and 3 2,000 times so as to obtain bootstrap distributions and the
   correspondingp-values.

Mark (1995) examines quarterly US dollar exchange rates for the Canadian dollar,
Deutsche Mark, Japanese yen and the Swiss franc and the corresponding funda-
mentals from 1973:2 to 1991:4. The last 40 quarters are used for the out-of-sample
forecasting exercise. His findings indicate that the hypothesis of no in-sample
predictability,H 0 :βk = 0 ∀k, can be rejected at the 5% significance level for

Switzerland and Germany. The slope coefficients, theR^2 s and the test statistics
tend to increase with the forecast horizon for all countries. Furthermore, in sev-
eral cases the monetary model forecasts are superior to the RW model, especially
for long horizons. Mark (1995) concludes that, given the small size of the dataset,
these results support the view that exchange rates are predictable.

22.6.1.1 Turning on the microscope

A number of subsequent studies questioned the validity of Mark’s methodology and
the resultant conclusions (see Neely and Sarno, 2002). An important assumption in
Mark’s study was that the process of the deviations of the exchange rate from its fun-
damental value is stationary. By the Granger representation theorem the exchange
rate and the fundamentals must posses a vector error correction model (VECM)
representation with cointegrating vector(1,− 1 ). The VECM model is expressed:

st=μs+λszt− 1 +

p∑− 1

i= 1

φisst−i+

p∑− 1

i= 1

ψisft−i+us,t, (22.83)

ft=μf+λfzt− 1 +

p∑− 1

i= 1

φifst−i+

p∑− 1

i= 1

ψifft−i+uf,t, (22.84)

whereλsandλfdetermine the speed of adjustment,μsandμfare intercepts,φi
andψiare parameters, and the disturbance termsus,tanduf,tare i.i.d. Station-
arity requires one of the speed of adjustment terms to be different from zero
andλf−λs<0.
Berkowitz and Giorgianni (2001) use the VECM representation and derive
the following expression for the slope coefficient in the long-horizon regression
(22.80):

βk=β 1

1 −θk

1 −θ

, (22.85)

whereθ= 1 +λf−λs<0 andβ 1 =λs. The above equation provides several insights
concerning long-horizon regressions under the assumption of a linear DGP. The
rejection of the null hypothesis that the slope coefficients in the long-horizon
regressions are zero implies that the exchange rate is weakly exogenous. In this
case, although the fundamentals do not contain predictive power, the existence of
a long-run relationship between fundamentals and the exchange rate is not ruled
out. It follows that, in the context of a linear model, the fundamentals cannot