Efthymios G. Pavlidis, Ivan Paya and David A. Peel 1061The MS model employed can be written as (see Hamilton, 1994):
rt=α(St)+β(St)fundt+εt, St=1,...,M, (22.93)wherertis the 12-month percentage change of the exchange rate and fundt
denotes the vector of RID fundamentals, which covers relative changes in money
supply, industrial production, money market interest rates and the government
bond yield. The vectors of coefficients,αandβ, are governed by the unobserv-
able state variable,St. In MS models the regime-generating process is an ergodic
Markov chain with a finite number of states,M, defined by the transition probabil-
itiespij=Pr(St+ 1 =j|St=i)with
∑M
j= 1 pij=^1 ∀i,j∈1,...,M. Frömmelet al.(2005)
set the number of states equal to two and assume that the error term,εt, is a white-
noise process with constant variance. The estimation of the model is implemented
by using an expectation maximization (EM) algorithm (Kim and Nelson, 1999).
Wald tests indicate that the null hypothesis of constant parameters can be
rejected for all exchange rates. For each exchange rate the coefficients are in line
with the RID model for one of the regimes. Furthermore, the MS-RID model pro-
duces a lower RMSE than the RW model. In contrast to the in-sample results, the
out-of-sample performance of the MS-RID model is not as encouraging. Fröm-
melet al.(2005) use a rolling sample of ten years and calculate the conditional
expectations of the percentage change of the exchange rate. Although the MS-
RID model is superior to the standard RID model, it cannot beat the naive
RW on the basis of theDM-statistic. This finding is not surprising, since non-
linear models in general, and MS models in particular, may produce superior
in-sample fits compared to linear models but not necessarily superior forecasts
(see Dacco and Satchell, 1999).
22.6.3 Real-time forecasting and market expectations
It is common practice in studies of exchange rate forecasting to employ the most
recent datasets on macroeconomic fundamentals. However, these datasets are sub-
ject to extensive revisions and are not available to real-time forecasters. Provided
that market participants’ expectations depend on currently available data on funda-
mentals, real-time data may lead to a better approximation of market expectations
than revised data (Neely and Sarno, 2002). According to the present value model
(22.61), exchange rates are influenced by market expectations of future fundamen-
tals and, therefore, real time data may improve upon the predictability of exchange
rates.
Faustet al.(2003) investigate the impact of using real time data for the currencies
examined by Mark (1995). Their findings indicate that long-horizon predictability
is present only in less than a two-year window around the vintage used by Mark. In
order to isolate the effect of data revisions from the sample period, the authors fix
the estimation and the forecast periods to be the same as Mark’s and use all vintages
of data from 1992 onward. Overall, the evidence of predictability weakens. As far as
real-time forecasting is concerned, the out-of-sample performance of the monetary
model is poor. The RMSEs are generally greater than those of the RW model and
increase with the horizon. However, real-time forecasts produce significantly lower