DISCUSSION PAPER SERIES
ZZZFHSURUJ
Available online at:
www.cepr.org/pubs/dps/DP3281.asp
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No. 3281
THE OUT-OF-SAMPLE SUCCESS OF
TERM STRUCTURE MODELS AS
EXCHANGE RATE PREDICTORS:
A STEP BEYOND
Richard Clarida, Lucio Sarno, Mark P Taylor
and Giorgio Valente
ISSN 0265-8003
THE OUT-OF-SAMPLE SUCCESS OF
TERM STRUCTURE MODELS AS
EXCHANGE RATE PREDICTORS:
A STEP BEYOND
Richard Clarida, Columbia University
Lucio Sarno, Warwick Business School and CEPR
Mark P Taylor, Warwick University and CEPR
Giorgio Valente, Warwick Business School
Discussion Paper No. 3281
March 2002
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CEPR Discussion Paper No. 3281
March 2002
ABSTRACT
The Out-of-Sample Success of Term Structure Models as
Exchange Rate Predictors: A Step Beyond*
A large literature suggests that standard exchange rate models cannot
outperform a random walk forecast and that the forward rate is not an optimal
predictor of the spot rate. There is evidence, however, that the term structure
of forward premia contains valuable information for forecasting future spot
exchange rates and that exchange rate dynamics display non-linearities. This
Paper proposes a term-structure forecasting model of exchange rates based
on a regime-switching vector equilibrium correction model which is novel in
this context. Our model significantly outperforms both a random walk and, to a
lesser extent, a linear term-structure vector equilibrium correction model for
four major dollar rates across a range of horizons.
JEL Classification: F31
Keywords: forecasting, foreign exchange, Markov switching, non-linearity and
term structure
Richard Clarida
Head of Economics Department
International Affairs Building
Room 1020
Columbia University
420 West 118th Street
New York, NY 10027
Tel: (1 212) 280 4648
Fax: (1 212) 854 8059
Email:
[email protected]
For further Discussion Papers by this author see:
www.cepr.org/pubs/new-dps/dplist.asp?authorid=102111
Lucio Sarno
Finance Group
Warwick Business School
University of Warwick
Coventry
CV4 7AL
Tel: (44 24) 7652 8219
Fax: (44 24) 7657 2871
Email:
[email protected]
For further Discussion Papers by this author see:
Mark P Taylor
Department of Economics
University of Warwick
Coventry
CV4 7AL
Tel: (44 24) 7657 3008
Fax: (44 24) 7652 3032
Email:
[email protected]
For further Discussion Papers by this author see:
www.cepr.org/pubs/new-dps/dplist.asp?authorid=100357
Giorgio Valente
Finance Group
Warwick Business School
University of Warwick
Coventry
CV4 7AL
Tel: (44 24) 7652 8537
Fax: (44 24) 7657 2871
Email:
[email protected]
For further Discussion Papers by this author see:
www.cepr.org/pubs/new-dps/dplist.asp?authorid=157421
* Forthcoming in the Journal of International Economics. This Paper was
partly written while Sarno and Taylor were visiting the Federal Reserve Bank
of St. Louis and the International Monetary Fund respectively. Sarno and
Taylor acknowledge financial support from the Economic and Social Research
Council (No. L138251044) and the Leverhulme Trust respectively. The
authors are indebted for their constructive comments to the discussants of the
Paper, Bruce Hansen and Philip Lane, as well as to Frank Diebold, Charles
Engel, Martin Evans, Lutz Kilian, Ken West, Jonathan Wright and other
participants to the conference on ‘Empirical Exchange Rate Models’, in
addition to partipants in seminars at the Federal Reserve Bank of St. Louis,
Washington University, the Bank of England, Queen Mary College, the
University of Manchester and the University of Warwick. The authors alone
are responsible for any errors and for the views expressed in the Paper.
NON-TECHNICAL SUMMARY
The Meese and Rogoff (1983a,b) studies marked a watershed in empirical
exchange rate economics. In particular, their robust finding that standard
empirical exchange rate models could not outperform a simple no-change
(random walk) forecast was at the time seen as devastating. Even with the
benefit of twenty years of hindsight, moreover, the random walk remains the
standard comparator for exchange rate forecasting and models which
consistently and significantly outperform a naive random walk are still elusive
(e.g. see Mark, 1995).
A parallel finding in the exchange rate literature, also dating from the early
1980s, was that the forward rate is not an optimal predictor of the future spot
exchange rate (see eg. Hansen and Hodrick, 1980; Frankel, 1980;
Bilson,1981), or equivalently that the forward premium is not an optimal
predictor of the rate of depreciation, as the efficient markets hypothesis, at
least in its risk-neutral formulation, would suggest. Attempts to locate the
source of this failure of the risk-neutral efficient markets hypothesis either in
the presence of stable, significant and plausible risk premia, or in some sense
in the failure of rational expectations when applied to the foreign exchange
market as a whole, have also met with mixed and very limited success. Thus,
from the early 1980s onward, exchange rate forecasting in general became
increasingly seen as a hazardous occupation, and this remains largely the
case.
A ray of hope in an otherwise murky environment was, however, provided by
Clarida and Taylor (1997), who argued that the failure of the forward rate
optimally to predict the future spot rate did not necessarily imply that forward
rates did not contain valuable information for forecasting future spot exchange
rates. Clarida and Taylor develop what they term an ‘agnostic’ framework for
linking spot rate and forward rate movements without assuming anything at all
specific about risk premia or expectations formation except that departures
from the risk-neutral efficient markets hypothesis (RNEMH) drive at most a
stationary wedge between forward and expected future spot rates. This is
sufficient to establish the existence of a linear vector equilibrium correction
model (VECM) for spot and forward exchange rates. Using this framework,
Clarida and Taylor are able to extract sufficient information from the term
structure of forward premia to outperform the random walk forecast – and a
range of alternative forecasts – for several exchange rates in out-of-sample
forecasting. Indeed, at the one-year forecasting horizon, their improvement
over the naive random walk is of the order of 40% in terms of root mean
square errors.
non-linearities of one sort or another in exchange rate movements has been
reported. One element of this, dating at least to Booth and Glassman (1987),
has been the mounting evidence that the conditional distribution of nominal
exchange rate changes is well described by a mixture of normal distributions
and that, consequently, a Markov switching model may be a logical
characterization of exchange rate behaviour. Although Markov-switching
models fit nominal exchange rate data very well, in general they do not
produce superior forecasts to a random walk or the forward rate on the basis
of conventional forecasting criteria. Overall, in fact, the literature on non-linear
modelling of exchange rates has produced models that fit satisfactorily and
forecast well in sample but that in general fail to beat simple random walk
models or linear specifications in out-of-sample forecasting (eg. Engel, 1994).
In the present Paper, we investigate whether allowing for non-linearities in the
underlying data-generating process for the term structure yields superior
exchange rate forecasts. This is done through estimating a fairly general
three-regime Markov-switching vector equilibrium correction model
(MS-VECM) for spot rates and the term structure of forward rates which is
essentially based on an extension of Markovian regime shifts to a
nonstationary framework, for which the underlying econometric theory has
recently been developed. Given the evidence of significant regime-switching
behavior in exchange rate movements discussed above, this seems a natural
way to extend the Clarida-Taylor analysis, even though this involves
estimating and forecasting from a sophisticated multivariate non-linear model.
Indeed, to the best of the present authors’ knowledge, the research reported
in this Paper represents the first application of Markov-switching in a
multivariate cointegrated framework to exchange rate modelling and
forecasting.
Using weekly data on spot and forward dollar exchange rates for the G5
countries over the period January 1979 through to December 1995, we found
strong evidence of the presence of non-linearities in the term structure, which
appeared to be modelled well by a multivariate three-regime Markov-switching
VECM that allows for shifts in both the intercept and in the covariance
structure. We then used this model to forecast dynamically out of sample over
the period January 1996 through to December 1998. The forecasting results
were impressive. The MS-VECM forecasts were found to be strongly superior
to the random walk forecasts at a range of forecasting horizons up to 52
weeks ahead, using standard forecasting accuracy criteria and on the basis of
standard tests of significance. Moreover, the non-linear VECM also
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Eurzq/ E1\1 dqg Pduldqr/ U1V1/ 4<;<1 Suhglfwruv lq G|qdplf Qrqolqhdu Prghov= Odujh Vdpsoh Ehkdylrxu/ Hfrqrphwulf Wkhru| 8/ 76307851
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Fodulgd/ U1K1 dqg Wd|oru/ P1S1/ 4<<61 Wkh Whup Vwuxfwxuh ri Iruzdug H{fkdqjh Suhplxpv dqg Wkh Iruhfdvwdelolw| ri Vsrw H{fkdqjh Udwhv= Fruuhfwlqj wkh Huuruv/ Qdwlrqdo Exuhdx ri Hfrqrplf Uhvhdufk Zrunlqj Sdshu Qr177751
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Fodun/ W1H1 dqg PfFudfnhq/ P1Z1/ 53341 Whvwv ri Htxdo Iruhfdvw Dffxudf| dqg Hqfrpsdvvlqj iru Qhvwhg Prghov/ Mrxuqdo ri Hfrqrphwulfv 438/ ;804431
Gdylhv/ U1E1/ 4<::1 K|srwkhvlv Whvwlqj zkhq d Qxlvdqfh Sdudphwhu lv Suhvhqw Rqo| Xqghu wkh Dowhuqdwlyh/ Elrphwulnd 97/ 57:05871
Gdylhv/ U1E1/ 4<;:1 K|srwkhvlv Whvwlqj zkhq d Qxlvdqfh Sdudphwhu lv Suhvhqw Rqo| Xqghu wkh Dowhuqdwlyh/ Elrphwulnd :7/ 660761
Ghpsvwhu/ D1 S1 / Odlug/ Q1 P1 dqg Uxelq/ G1 E1 / 4<::1 Pd{lpxp Olnholkrrg Hvwlpdwlrq iurp Lqfrpsohwh Gdwd Yld wkh HP Dojrulwkp/ Mrxuqdo ri wkh Ur|do Vwdwlvwlfdo Vrflhw| 6< Vhulhv E/ 406;1
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Glherog/ I1[1 dqg Qdvrq/ M1D1/ 4<<31 Qrqsdudphwulf H{fkdqjh Udwh SuhglfwlrqB/ Mrxuqdo ri Lqwhuqdwlrqdo Hfrqrplfv 5;/ 64806651
Hqjho/ F1/ 4<<71 Fdq wkh Pdunry Vzlwfklqj Prgho Iruhfdvw H{fkdqjh UdwhvB/ Mrxuqdo ri Lqwhu0 qdwlrqdo Hfrqrplfv 69/ 48404981
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Hydqv/ P1G1G1 dqg O|rqv/ U1N1/ 53351 Rughu Iorz dqg H{fkdqjh Udwh G|qdplfv/ Mrxuqdo ri Srolwlfdo Hfrqrp| 443/ 4:304;31
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Kdplowrq/ M1G1/ 4<<61 Hvwlpdwlrq/ Lqihuhqfh dqg Iruhfdvwlqj ri Wlph Vhulhv Vxemhfw wr Fkdqjhv lq Uhjlph/ lq= Pdggdod/ J1V1/ Udr/ F1U1 dqg Ylqrg/ K1G1 +Hgv1,/ Kdqgerrn ri Hfrqrphwulfv/ Yro17/ Hovhylhu/ Dpvwhugdp1
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Kdqvhq/ E1H1/ 4<<91 Huudwxp= Wkh Olnholkrrg Udwlr Whvw xqghu Qrqvwdqgdug Frqglwlrqv= Whvwlqj wkh Pdunry Vzlwfklqj Prgho ri JQS/ Mrxuqdo ri Dssolhg Hfrqrphwulfv 44/ 4<804<;1
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47Wkh EGV whvw iru d vhulhvx
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48 Zh dovr frpsduh ehorz wkh iruhfdvwlqj shuirupdqfh ri wkh olqhdu YHFP wr wkdw ri dq
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53Wkhvh hvwlpdwlrq uhvxowv duh qrw uhsruwhg wr frqvhuyh vsdfh/ exw wkh| duh dydlodeoh lq Fodulgd/
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54 Lqyhvwljdwlrq ri wkh hvwlpdwhg vprrwkhg wudqvlwlrq suredelolwlhv +qrw uhsruwhg wr frqvhuyh
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55Zh dovr orrnhg dw judskv ri vwdqgdugl}hg uhvlgxdov/ wkh vprrwkhg uhvlgxdov dqg wkh rqh0vwhs
suhglfwlrq huuruv iurp hdfk hvwlpdwhg PVLK0YHFP1Wkh glhuhqfh lv frqfhuqhg zlwk wkh zhljkwlqj ri wkh uhvlgxdov1Orrvho| vshdnlqj/ wkh vprrwkhg uhvlgxdov duh wkh forvhvw wr wkh vdpsoh uhvlgxdov iurp d olqhdu uhjuhvvlrq prgho> krzhyhu/ wkh| ryhuhvwlpdwh wkh h{sodqdwru| srzhu ri wkh Pdunry0 vzlwfklqj prgho gxh wr wkh xvh ri wkh ixoo0vdpsoh lqirupdwlrq fryhuhg lq wkh vprrwkhg uhjlph yhfwru1Wkh vwdqgdugl}hg uhvlgxdov duh frqglwlrqdo uhvlgxdov1Wkh rqh0vwhs suhglfwlrq huuruv duh edvhg rq wkh suhglfwhg uhjlph suredelolwlhv1Xqiruwxqdwho|/ pdq| frqyhqwlrqdo gldjqrvwlf whvwv/ vxfk dv vwdqgdug uhvlgxdo vhuldo fruuhodwlrq whvwv/ pd| qrw kdyh wkhlu frqyhqwlrqdo dv|pswrwlf glvwulexwlrq zkhq wkh uhvlgxdov frph iurp Pdunry0vzlwfklqj prghov dqg duh wkhuhiruh qrw uhsruwhg khuh1Krzhyhu/ wkh judskv ri vwdqgdugl}hg uhvlgxdov/ wkh vprrwkhg uhvlgxdov dqg wkh rqh0vwhs suhglfwlrq huuruv surylghg qr ylvxdo hylghqfh ri uhvlgxdo vhuldo fruuhodwlrq lq dq| ri wkh uhvlgxdov vhulhv sorwwhg1
56Iru d ghvfulswlrq ri wkh surfhgxuh ri rxw0ri0vdpsoh iruhfdvwlqj lq d Pdunry0vzlwfklqj iudph0
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57Vhh Eurzq dqg Pduldqr +4<;7/ 4<;<, dqg/ iru d jhqhudo glvfxvvlrq/ Judqjhu dqg Whudvyluwd
+4<<6/ Fkdswhu ;, dqg Iudqvhv dqg ydq Glmn +5333/ Fkdswhuv 607,1
58Wkh uxoh lv lpsohphqwhg dv iroorzv= zh hvwlpdwhg dq DU+4, prgho wr wkh txdqwlw|gwrewdlqlqj
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59Fodun dqg PfFudfnhq +5334, ghulyh wkh dv|pswrwlf glvwulexwlrqv ri wzr vwdqgdug whvwv lq wklv
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Wdeoh 51 Orqj0uxq htxloleulxp sdudphwhuv
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