Wolff, Christian C.P.

English

Research Papers in Economics

International  Jouma;  of Forecasting  4 (1988) 605-607 
North-Holland 
MODELS OF EXCHANGE RATES 
A Comparison of Forecasting Results 
Christian  C.P.  WOLFF 
London  Business  School.  London  NW/  4SA.  UK 
Unklersiy  cf  Limburg,  Maastricht.  The Netherlands 
A bstract:  In  this  note  we  compare  the  results  of  several  published  papers  on  exchange  rate 
forecasting.  With  regard  to univariate  time  series  models,  we confirm  the result  that  such 
models,  on  average,  do  not  outperform  the  simple  random  walk  forecasting  rule.  This 
conclusion  corrects  results  reported  in  this  Journal  by Alexander  and  Thomas  (1987). 
Keywords:  Exchange  rates,  Kalman  filter,  Random  walk,  Forecasting  results,  Comparison. 
1. Introduction 
Meese  and  Rogoff  (1983a)  studied  the  forecasting  performance  of  several  important  monetary 
models  of  exchange  rate  determination.  Although  in-sample  studies  of  these  models  usually  show 
quite  satisfactory  fits.  Meese  and  Rogoff’s  out-of-sample  results  were  not  very  encouraging:  the 
structural  models  failed  to  improve  upon  the  simple  random  walk  forecasting  rule,  even  though  the 
model’s  forecasts  were based  on  actual,  realized  values  of  future  explanatory  variables.  Wolff  (1987) 
applied  varying  parameter  estimation  techniqr:es,  based  on  recursive  application  of the Kalman  filter, 
and  found  that  the  introduction  of  parameter  variation  marginally  enhances  the  various  models’ 
forecasting  performance. 
In  a recent  article  in  this  ~ozamal, Alexander  a&  Thomas  (1987) update  the  Meese  and  Rogoff 
(1983a)  results  and  evaluate  the  use  of  time  varying  parameters  to  improve  the  models’  forecasting 
performance.  Their  empirical  results  for  time  series models  differ  dramatically  from  previous  studies 
due  to  a computational  error. 
2. Comparing various  studies 
Alexander  and  Thomas  (1987)  present  out-of-sample  forecasting  results  for  two  differen_+ time 
series models.  The  first is an AR(l)  model  for first  differences  in the  (log of  the  ) spot  exchange  rate 
CL  = a + b(S,_,  -  S,_,)  + e,,  (3) 
e second is an  A 
s,  - q-1  =a+b(S,_,  -  S,_,)  + c(S,_,  -  S,_,)  + e,.  (4 
0169-2070/88/$3.50  +Y  1988. Elsevier Science  Publishers  B.V. (North-Holland) 606  C. C. P.  Wo,ff  /  Models  of exchange  rates 
Alexander  and  Thomas  reported  both  U-statistics  and  RMSEs  on  the  models’  ability  to  predict 
future  spot  exchange  rates. 
When  comparing  Alexander  and  Thomas’  results  with  those  reported  by  Meese  and  Rogoff 
(1983a). two  striking  conclusions  emerge.  First,  _.*-  the  RMSEs  for  the  longer  horizons  are  not  greater 
than  those  for the  shorter  horizons.  Second,  all U-statistics  are in the range  0.63-0.80,  indicating  that 
for  all forecasting  horizons  and  all currencies  the  estimated  time  series  models  perform  better  than 
the  simple  random  walk  forecasting  rule  by  a  substantial  margin.  These  results,  if  true,  would 
strongly  contradict  the  Meese and  Rogoff  (1983a) cc nclusion. 
It  appears  however,  that  Alexander  and  Thomas’  results  were  incorrect.  We  have  repeated  the 
exact  forecasting  experiment  performed  by  Alexander  and  Thomas  for  the  two  time  series  models. 
Our exchange  rate  data  are taken  from  the International  Financial Statistics  (IFS).  The  correct  results 
are presented  in  table  1. 
The  results  in table  1 roughly  confirm  Meese and  Rogoff’s  conclusion:  on  average  the  ti,me series 
models  do  not  improve  upon  the  random  walk  forecasting  rule.  Note,  however,  that  the  time  series 
models  do  outperform  the  random  walk  for  the  dollar/sterling  exchange  rate.  Note  also  that  the 
RMSEs  in  table  1 exhibit  the  usual  increasing  pattern  as the  forecasting  horizon  is extended. 
Table 1 
Out-of-Sample forecasting results a of time series models based on  IFS  data. 
Model  Horizon (months) 
1  3 
(A)  Root  mean  square  forecast  errors  - 
6  12  24  36 
Dollar/Mark 
AR(l) 
AN21 
Dollar,/  Yen 
AR(l) 
AR(2) 
.r)ollar/Pound 
AR(l) 
AN21 
(B)  U-statistics 
Dollar/  Mark 
AR(l) 
AN2) 
Dollar/  Yen 
AR(l) 
AN21 
Dollar/  Pound 
.-  .~ 
AK\!) 
AN21 
3.57  r.72  10.32  16.34  27.00  39.41 
3.58  6.65  10.27  16.36  27.06  39.56 
3.44  6.07  8.46  10.54  13.80  16.64 
3.47  6.10  8.47  10.53  13.78  16.64 
3.60  6.58  10.57  14.43  23.86  36.54 
3.58  6.55  10.58  14.47  23.84  36.59 
1.04  1.07  1.11  1.20  1.32  1.42 
1 .n4  1.06  1.10  1.20  1.32  1.42 
1.01 
1  .Ol 
1.01 
1  .O? 
1.03 
1.04 
1.12 
1.12 
1.41 
1.40 
1.71 
1.71 
.  n- 
1.W 
1  .oo 
0.99  0.98  0.91  0.88  0.91 
0.98  0.98  0.91  0.88  0.91 
a  Period: January  1980-October  1985. C. CT  P.  rVolff /  Model’s  of exchange  rates  607 
References 
Alexander,  Don  and  Lee R. Thomas  III,  1987. Monetary/asset  models  of exchang;  rate  determination:  How well have  they 
performed  in  the 1980’s?, International  Journal  of Fcbrecasting 3, 53-64. 
Meese, Richard  A. and  Kenneth  Rogoff,  19S3a, Empirical  exchange  rate  models of the seventies:  Do they fit out  of sample?, 
Journal  of  International  Economics  14, 3-24. 
Meese.  Richard  A.  and  Kenneth  Rogoff,  1983b,  the  out-of-sample  failure  of  exchange  rate  models:  Sampling  error  or 
m&specification?,  in:  Jacob  A.  Frenkel,  ed.,  Exchange  rates  and  international  macroeconomics  (University  of  Chicago 
Press, Chicago,  IL) 67-105. 
Wolff,  Christian  C.P.,  1987, Time-varying  parameters  and  the out-of-sample  forecasting  performance  of structural  exchange 
rate  models,  Journal  of Business and Economic Statistics 5, 87-97. 
Biog/,aphy:  Christian  WOLFF  is  Professor  of  Finance  at  the  University  of  Limburg,  Maastricht, 
The  Netherlands,  and  Research  Fellow  in  International  Finance  at the  London  Business 
School.  He obtained  a Ph.D.  from  the  Graduate  School  of  Business  at the  University  of 
Chicago  in  1985.  His  main  research  interest  is  in  international  financial  markets. 
Previous  publications  include  articles  in  the  Journal of Finance, the  Journal of Business 
and Economic Statistics,  the  Journal of International Money and Finance and  Economics 
Letters. 

1983b, the out-of-sample failure of exchange rate models: Sampling error or m&specification?,

Monetary/asset models of exchang; rate determination: How well have they performed in the 1980’s?,

Time-varying parameters and the out-of-sample forecasting performance of structural exchange rate models,

WOLFF is Professor of Finance at the University of Limburg, Maastricht, The Netherlands, and Research Fellow in International Finance at the London Business School. He obtained a Ph.D. from the Graduate School of Business at the University of Chicago in

Models of exchange rates. A comparison of forecasting results.

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Models of exchange rates. A comparison of forecasting results.

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