Palgrave Handbook of Econometrics: Applied Econometrics

Efthymios G. Pavlidis, Ivan Paya and David A. Peel 1063

wherexjo,tdenotes order flow from end-user segmentj. Six end-user segments are
considered: trades implemented in the US and non-US markets for non-financial
firms, investors and leveraged trades. The forecasting performance of the micro-
based model is compared to that of an RW and a structural model using data for
the largest spot market, the US dollar/euro, for the period from 1993 to 1999.
In general, the findings indicate that, for horizons between 10 and 20 days, the
micro-based models are able to beat the RW benchmark and the structural model,
irrespective of the type of order flow used.
Large values of the discount factor and highly persistent fundamentals provide
an explanation for the failure of structural models in out-of-sample forecasting.
However, forecastability of the changes in the exchange rate is still possible in the
presence of stationary terms. Consider the present value model (22.61) and let
ft=a′ 1 xtanda′ 2 xt=rpt. If the deviations from the UIP,rpt, follow a stationary
AR(1) process:

rpt=θrpt− 1 +et, (22.99)

whereet∼i.i.d. andσe^2 =var(et), andftis an RW process, with innovationηt

andση^2 =var(ηt), then the forward solution for the exchange rate is:

st=ft+

b

1 −bθ

rpt. (22.100)

Thek-period change in the exchange rate is:

st+k−st=ft+k−ft+

b

1 −bθ

(rpt+k−rpt)

=

∑k

j= 1

ηt+k+

b

1 −bθ

(θk− 1 )rpt+

b

1 −bθ

∑k

j= 1

θk−jet+k (22.101)

=

∑k

j= 1

ηt+k+( 1 −θk)zt+

b

1 −bθ

∑k

j= 1

θk−jet+k,

whereztare the deviations from the observed fundamentals, and the correspond-

ingR^2 kis:

R^2 k=

(θk− 1 )^2 var(ft)

var(st+k−st)

=

( 1 −θk)^2 σe^2

( 1 −θk)^2 σe^2 +( 1 −θ^2 k)^2 σe^2 +k( 1 −θ^2 )( 1 −bθ)^2 ση^2 /b^2

. (22.102)

Engelet al.(2007) setb=0.9,θ=0.95 andση/σe=3 and calibrate the model. They

find that predictability, in terms ofR^2 k, exhibits a hump shaped pattern with respect

tok. At short horizons there is not much evidence of predictability, e.g.,R^21 =0.02,