Palgrave Handbook of Econometrics: Applied Econometrics

Efthymios G. Pavlidis, Ivan Paya and David A. Peel 1057

contain predictive power at long horizons without the presence of short-run pre-
dictability, given thatβ 1 =0 impliesβk= 0 ∀k. Thus, either Mark’s results are
spurious, or the DGP is misspecified.^63
Spurious inference may arise due to the fact that Mark’s procedure is based on
the assumption that the deviation process is stationary. Conditioning on cointe-
gration when cointegration fails may result in false inferences. The LS estimates
of the long-horizon regression will be inconsistent without having any economic
interpretation and conventional statistical tests will not be valid, especially for
long-horizons (see Berben and van Dijk, 1998). Letstfollow an RW: it follows that,
for largek, the dependent variablest+k−stwill also approximate an RW. Given
thatzt∼I( 1 ), the long-horizon regression involves regressing anI( 1 )variable on
anotherI( 1 )variable. This gives rise to a near-spurious regression problem (Granger
and Newbold, 1974).^64 To this end, Berkowitz and Giorgianni (2001) apply the
Horvath–Watson test (Horvath and Watson, 1995) without being able to reject
the null of no cointegration for all countries except Switzerland. It is noted, how-
ever, that if the deviation process is, in fact, nonlinear then linear cointegration
techniques may suffer from low power (Paya and Peel, 2007a).
Kilian (1999) emphasizes that the stability of the bootstrap DGP is not ensured in
the procedure proposed by Mark. To this end, he suggests feasible generalized least
squares (FGLS) estimation subject to a stability constraint. Furthermore, he notes
that Mark’s approach is inconsistent and may result in spurious inference due to
the fact that a drift is included in the bootstrap exchange rate series but forecasts
are based on the no-change model. Thus, the superior forecast performance of the
long-horizon regression may be due to either the contribution of the fundamentals
or just the inclusion of the drift term. The VECM bootstrap proposed consists of
the following steps:

1. Define the VECM model as the DGP:

st=μs+λszt− 1 +

p∑− 1

i= 1

φsist−i+

p∑− 1

i= 1

ψsift−i+us,t,

ft=μf+λfzt− 1 +

p∑− 1

i= 1

φfist−i+

p∑− 1

i= 1

ψifft−i+uf,t.

2. Impose the null that all the coefficients in the first equation except for the
   intercept are zero and specify the lag order by using an information criterion
   such as the AIC. Estimate the model by FGLS subject to the stability constraint.


3. Use the coefficient estimates and draw with replacement from the observed
   recentered residuals to recursively generate pseudo-observations forstandft.


4. Estimate the long-horizon regressions for the pseudo-series and construct the
   test statistics under examination.


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