a comparison of alternative exchange rate forecasting models

A Comparison of Alternative Exchange Rate Forecasting Models *

LINDSAY I. HOGAN Bureau of Agricultural Economics,

Canberra, ACT 2601

This paper compares a number of structural and times4eries models on the basis of their accuracy in forecasting the Australian- US dollar exchange rate out of sample. Purchasing power parity, forward exchange theory, static and dynamic specifications of both the flexible price and sticky price monetary models. and univariate ARIMA moaels are considered in the paper. Exchange rate forecasts are generated at horizons of one to four quarters. In contrast to overseas results which support the view that the exchange rate follows a random walk, several models in this study are found to generate forecasts superior to the random walk model.

I Introduction The floating of major international currencies

in 1973 was accompanied by a heightened interest in exchange rate modelling. Structural models, in particular the monetary model, appeared for several years to explain exchange rate movements reasonably well. However, the fitted performance of these models deteriorated after about 1978 (Frankel, 1982; Adam, 1983). Previous studies of exchange rate models have typically been limited to within-sample comparisons. The major exception to this approach was the study by Meese and Rogoff (1983), which compared a number of time-series and structural models on the basis of out-of-sample forecasting accuracy. They found a random walk model performed as well as the estimated exchange rate models for major US dollar exchange rates.’ These results cast doubt on

* An earlier version of this paper was presented at the 14th Conference of Economists, University of New South Wales, 13-17 May 1985. I am grateful to Michael Kirby for helpful comments.

These included exchange rates with the pound sterling, the Deutschmark and the yen. as wcU as the US trade-weighted exchange rate.

the usefulness of the current set of exchange rate models. However, given the importance of exchange rate movements to Australia’s export- and import-competing industries and, hence, to the general economy, it seems worthwhile to continue research in this area.

In Australia a number of exchange rate regimes have been adopted over the past decade, the trend being toward more market-oriented systems of exchange rate determination. Until September 1974 the Australian currency was tied to the US dollar. Since then the value of the Australian dollar has varied against all currencies including the US dollar. Initially there was a futed link to the average value of a trade-weighted ‘basket’ of currencies. From 29 November 1976 this was replaced by a variable trade-weighted index. In December 1983 a floating exchange rate arrangement was introduced, whereby market forces determined the value of the Australian dollar, although the Reserve Bank retained the discretion to intervene. In this paper the Australian-US dollar exchange rate is examined over the period December quarter 1974 to the June quarter 1984, thus covering a period of varying bilateral exchange rate regimes. A number of exchange rate models are compared on

215

216 THE ECONOMIC RECORD JUNE

the basis of their accuracy in forecasting the Australian-US dollar exchange rate out-of-sample. The various structural and time-series models are briefly reviewed in Section 11. The techniques used to compare out-of-sample forecasts and a description of data are given in Section 111. Section IV contains the results of the study. Some concluding comments are made in Sec:ion V.

I1 Exchange Rate Models The structural models chosen for this study

include the flexible price monetary model (Frenkel, 1976; Bilson, 1978) and the sticky price monetary model (Frankel, 1979b; Dornbusch, 1976). One of the possible explanations for the poor results obtained by previous studies is mis-specification of the demand for money equations. Separate research has indicated that it may be more appropriate to base monetary models on demand for money equations which incorporate a partial adjustment mechanism. Thus, dynamic specifications of the flexible price monetary model and the sticky price monetary model also are included. In addition, exchange rate forecasts are generated from both purchasing power parity and interest parity conditions. These formulations, as well as forming important building blocks to the monetary models, continue to be popular in practice, perhaps partly because of the ease with which they can be manipulated in ‘back-of-the-envelope’ calculations. Time-series methods also are incorporated in the study, with the random walk model viewed as a point of reference in judging the forecasting performance of other models.

Purchasing Power Parity Theory The relative purchasing power parity theory

states that the ratio of the equilibrium exchange rate, E (units of domestic currency per unit of foreign currency), in the current period to the equilibrium exchange rate in the base period, denoted by subscript 0, is determined by the ratio of the domestic price index, P, in the current period to the foreign price index, P, in the current period, where each price index has base period 0 (Officer, 1978), that is,

E = E$/P*. (1)

e = eo + (p - p * ) (2) where e, p and p* are the logs of E, P and P, respectively. An equation of purchasing power

Equation (1) may be written in logarithmic form as

parity which may be estimated is

e = a , + a , @ - p * ) + u (3) where u is a random error term. For purchasing power parity to hold perfectly, a, should equal one and a,, equal eo. Absolute purchasing power parity asserts that the equilibrium exchange rate is determined by the relative price levels but this version is difficult t o test since price data are typically in index form.

This specification assumes instantaneous adjustment of the exchange rate to changes in relative prices. It may be more realistic to assume there is lagged adjustment. Assume then that the long-run equilibrium value of the exchange rate, 2, is given by

(4)

Also assume that a partial adjustment process holds such that the exchange rate, during the current period, moves partly toward its long-run equilibrium value

e - e - , = g ( & e - , ) + u O<g<l ( 5 )

where g is the adjustment parameter. The closer g is to unity, the greater is the adjustment made in the current period. Combining equations (4) and ( 5 ) gives a dynamic specification of purchasing power parity

e = a & + a , g @ - p * ) + ( l - g ) e _ , + u . ( 6 ) Note that equation (6) contains a simple disturbance term. Evidence of substantial deviations from purchasing power parity during the past decade is well documented (Frenkel, 1981)’.

Forward Exchange Theory This is also known as interest rate parity theory

(Isard, 1978). Assume that perfect international capital mobility exists and bonds are free of default risk (political or confiscation risk), both domestically and abroad. Under these conditions, foreign bonds with forward cover are perfect substitutes for domestic bonds. Ignoring transactions costs, arbitrageurs in pursuit of profit will move funds to bring the domestic interest rate relative to the foreign interest rate into equality with the forward premium on foreign exchange. Covered interest parity may be written in logarithmic form as

(7)

>=ao + a, (p - p * ) .

f- e = ln(1 + r ) - ln(1 + r*) 2 See Officer (1976) for a comprehensive review of

purchasing power parity theory.

1986 EXCHANGE RATE FORECASTING 217

where f is the log of the forward exchange rate (units of domestic currency per unit of foreign currency) and rand P are the domestic and foreign nominal interest rates, respectively. The variables

r a n d P are defined over the same time interval. Frenkel and Levich (1975) found that deviations from covered interest parity are smaller than transactions costs.

The forward rate may differ from the expected future spot rate by a risk premium. Assume, however, that attitudes toward exchange risk are characterized by risk neutrality such that speculators are risk neutral or exchange risk is perfectly diversifiable (Frankel, 1979a). In this case, speculators in pursuit of profit will bring the forward rate into equality with the expected future spot rate, E(e)

E ( e ) = f . , (8) Combining equations (7) and (8) gives the stronger uncovered interest parity condition

E ( e ) - e = I n ( ] + r ) - In(1 + P ) . (9) Empirical tests of uncovered interest parity usually assume perfect foresight so the expected future spot rate is replaced by the actual realized future rate, e,. Several studies have concluded, on this basis, that the forward exchange rate is a biased predictor of the future spot rate (Hansen and Hodrick, 1980; Baillie ef al., 1983). However, Turnovsky and Ball (1983) provide some support for the speculative efficiency hypothesis.

Asset Market Models wifh Static Specification of the Demand for Money Equations

Assuming there is instantaneous adjustment in the demand for money to changes in real income and nominal interest rates, the money demand equations are

m - p = a, + a , y - a2r + u (10) m + - p * = a d + a f y + - a ; P + u + (11)

where m is the log of the domestic money supply, y is the log of the domestic real income and an asterisk denotes a corresponding foreign variable.

Taking the difference of the demand for money equations in (10) and (11) .

( m - m*) - (p - p * ) = a, - ad + a,y - afy+

- u2r + u i P + u - u* . (12) Assume purchasing power parity holds in the short run. Incorporating equation (2) into (12)

e = (m - m*) + e, - a. + ad - a,y + a:y* + a,' -a ,+r*+v (13)

where v is a random error term equal to u* - u. Assuming equal elasticities for the corresponding domestic and foreign variables3, that is, a, = af and a2 = a?,

e = (m - m+) + b, - b,O, - y*) + b,(r - P ) + v. (14)

An increase in the domestic nominal interest rate relative to the foreign interest rate results in a depreciation of the domestic currency. This result is contrary to intuition and it may be useful to interpret it in terms of the Fisher parity condition. The Fisher condition states that the real interest rate is equal to the nominal interest rate, less the expected rate of inflation. If real interest rates are assumed to be equalized through international capital mobility, the nominal interest rate differential will equal the expected inflation differential. Thus, a relative increase in the domestic nominal rate of interest will coincide with an increase in the expected inflation differential, resulting in a depreciation of the domestic currency.

Given that there is substantial evidence of deviations from purchasing power parity in the short run (Frenkel, 1981), the sticky pnce monetary model may provide a more realistic alternative to the flexible price model. Assume prices are sticky in the short run, but purchasing power parity holds in the long run, such that

k & + ( i J -L, '). (15)

Combining this long-run purchasing power parity assumption with the difference of the money demand equations in (12) and relabelling the disturbance term

P= (* rir') + co - c ,G - j . ) + c*(?- i*) + v. (16)

It is assumed that the exchange rate is expected, in the short run, to move partly toward its long- run equilibrium value and, in the long run, to change at the rate of the expected long-run inflation differential @ -$*); that is

E(e) - e = k(& e) + (3, - j*) (17)

3 In this study, these linear restrictions are accepted at the 5 per cent level of significance. Analogous restrictions are also adopted in the other monetary exchange rate models.


In addition, uncovered interest parity is assumed to hold approximately, such that

E(e) - e = r - P. (18) Combining the assumptions in (17) and (18)

e - e = k - ' [ ( r - B ) - ( P - ; * ) ] (19)

so the gap between the spot exchange rate and its long-run equilibrium value is a function of the real interest rate differential.

In the long run when e = e , it follows that i- iZ =i) -B*. Thus, the long-run interest differential in equation (16) is replaced by the expected long-run inflation differential.4 Incorporating also the assumption in (19) into equation (16)

e = (m - m*) + do - d,O, - y*) - d2(r - r*) + d3(j,-B*)+ Y (20)

where the money supply and income variables are assumed, in the current period, to be at their long- run values. In this model a n increase in the domestic rate of interest relative to the foreign interest rate results in an appreciation of the domestic currency, while a relative increase in the expected long-run domestic inflation rate results directly in a depreciation o f the domestic currency.

Asset Market Models with Dynamic Specification of the Demand for Money Equations

Empirical evidence does not appear to support the assumption of instantaneous adjustment in money demand to changes in its explanators (Pagan and Volker, 1981). Incorporating a partial adjustment mechanism, the demand for money equations can be rewritten

m - p = a, + a,y - azr + a,(m - p ) - I + u (2 I ) m+ -p* =a: +ay;'-arf + a3(m* - p * ) - I + u*.

(22) Taking the difference of the demand for money

equations in (21) and (22), assuming short-run purchasing power parity holds exactly as given in equation (2) and assuming the domestic and foreign parameters are equal

e = ( m - m * ) + b , - b ,O , -y* )+b , ( r - r* )+b ,e_ ,

- b,(m - m * ) - , + v . (23)

This result is also useful in the estimation stage as it enables the long-term intaest rate differential to be wd as a proxy for the expected long-run inflation differential.

This differs from the static specification of the flexible price monetary model given in equation (14) by the addition of a lagged exchange rate term and a lagged relative money supplies term.

Assume that purchasing power parity holds in the long run, as given in equation (15). Combining this assumption with the difference of the money demand equations in (21) and (22) results in

e= (rn - rn * ) + c, - C 1 ( i , - E * ) + cz(i - i*)

+ c,e- I - c4(* - m*)- 1 + v . (24) Incorporating similar assumptions to those set out for the sticky price monetary model, equation (24) becomes

e = (m - m*) + do - d,O, - y*) - d2(r - P )

This specification,of the model also includes lags of the interest differential and the expected long- run inflation differential.

Time-Series Models The random walk is one model within the class

of univariate time-series models and is used in this study as a point of reference. Major international organizations, such as the OECD, typically assume no change in exchange rates over the forecast horizon. Theoretical support for this approach stems from the theory of rational speculative behaviour. This theory suggests that flexible exchange rates follow a random walk since unanticipated information, used in forming expectations of the exchange rate, is random and independent of past events (Poole, 1967). Empirical support for a no-change extrapolation is provided by Meese and Rogoff (1983). They found that exchange rate models failed to forecast more accurately out-of-sample than a random walk model. In addition to the random walk, forecasts are generated from ARIMA models which are fitted to the log of the Australian-US dollar exchange rate."

5 Multivariate time-series techniques are not considered in the current paper. In separate research a vector autoregressive forecasting model of the US- Australian dollar exchange rate was derived (Hogan. Urban and A&, 1985). While the within-sample fits were satisfactory, the out-of-sample forecasting performance of the estimated model was found to be clearly inferior to the naive no-change extrapolation of the random walk model.


III Experimental Design and Data The Australian-US dollar exchange rate is

modelled over the period from 1974 (4) to 1984 (2) using quarterly data. Quarterly observations are preferred as underlying trends are judged to be more readily identifiable in quarterly data compared with monthly data. In addition, some data series, such as the Australian consumer price index, are available only on a quarterly basis. (It may be noted, however, that several models were estimated with monthly data but, since the results were similar to those based on quarterly data, they are not reported in the paper.) The various exchange rate models are initially estimated by ordinary least squares (OLS) over the period 1974 (4) to 1981 (3) with forecasts subsequently derived for horizons of one, two, three and four quarters, respectively, using actual realized values of the explanatory variables. The estimation period is then extended by one quarter to cover the period 1974 (4) to 198 1 (4) and forecasts are again generated for the four time horizons. The estimation period is extended by a quarter a t a time, with forecasts derived at each step until the final estimation period of 1974 (4) to 1984 (1) is reached. In this way a set of forecasts is obtained for the horizons of one, two, three and four quarters.

Problems associated with seasonal adjustment processes have been highlighted in the literature. Structural parameter estimates may be distorted when the variables are not all adjusted by the same method (Sims, 1974). The data used in this study are seasonally unadjusted and a set of seasonal dummies is included in the equations. Industrial production is used as a proxy for real income since seasonally unadjusted real gross national product data are unavailable for the United States.

The spot Australian-US dollar exchange rate used is the quarterly average of daiIy mid-rates quoted by the Commonwealth Trading Bank. The Reserve Bank three-month and six-month forward exchange rates are used for the period ending September 1983, after which the corresponding National Bank forward rates are used. The consumer price index is used in the purchasing power parity equations. In the uncovered interest parity equation, the Australian 90-day bank accepted commercial bill rate and the US three- month Treasury bill rate are used to forecast the exchange rate one quarter ahead, and the corresponding 180-day and six-month rates are used to forecast the exchange rate two quarters ahead. In the monetary models, the short-term interest rates are given by the Australian 90-day

bank accepted commercial bill rate and the US three-month Treasury bill rate. The long-term interest rate differential is used as a proxy for the expected long-run inflation differential. Long-term interest rates are given by the yield on Australian ten-year Commonwealth government bonds and US ten-year or more government security yields. Australian M3 and US A41 were chosen as the money supply variables, as they correspond most closely by definition.

The accuracy of the out-of-sample forecasts are measured on the basis of mean error (ME), mean absolute error (MAE) and root mean squared error (RMSE), defined as

N k - I

s = o

N k - I

MAE = ' l F t + s + k - A l + s + k l / N k k = s = o

s = o k = 1,2,3,4

where k denotes the forecast horizon, Nk t1.d total number of forecasts, F, the forecast value, Atthe actual value and forecasting begins in period f .6

I V Empirical Results The estimated exchange rate equations are

presented in Table 1. Very poor results are obtained for the short-run purchasing power parity equation. Assuming a partial adjustment mechanism however, results in a long-run elasticity of the exchange rate with respect t o relative prices of 0.928. In each of the monetary exchange rate equations a test of the restriction on the coefficient of the money supply growth differential was rejected at the 5 per cent signficance level. In these equations, all the coefficients which are found to be statistically significant have the correct sign. However, several coefficients are not significantly different from zero. The static monetary equations produce extremely poor fits and only the real income differential has a statistically significant impact on the exchange rate. Estimation of the dynamic mometary equations produce slightly better results, largely reflecting the inclusion of the lagged exchange rate as an explanatory variable.

6 See Meese and Rogoff (1983) for a further discussion of these statistics.


TABLE 1 Estimated Structural Exchange Rate Equations: 1974(4) to 1981(3)

Constant

P-P*

m - m *

Y -Y*

r - r +

6-j'

e- I

(rn-m*)-I

( r - r.7- 1

G -P) - l First quarter .

dummy

Second quarter dummy

Third quarter dummy

Rho1

Adjusted R2 DW SER

-0.141 ( - 4.96)

0.523 (1.57) -

- -

-

-

-

-

-

-

-

-

0.846 (9.69) 0.05 1.49 0.02

- 0.07 I ( - 3.33)

0.440 (2.24)

-

-

-

-

0.526 (4.26)

-

-

-

-

-

-

0.371 (2.19) 0.71 0.28(a) 0.02

- 1.493 ( - 1.28)

-

0.283 (1.16) - 0.592

( - 3.08) 0.006

(1.63) -

-

-

- -

- 0.044 ( - 2.83)

- 0.018 ( - 1.36)

- 0.007 ( - 0.73)

0.753 (6.04) 0.2 I 1.48 0.02

- 1.449 ( - 1.24)

-

0.284 (1.13) - 0.592

( - 3.00) 0.006

(1.10) 0.001

(0.07) -

-

- -

- 0.044 ( - 2.75)

- 0.017 ( - 1.18)

- 0.007 ( - 0.70)

0.754 (6.06) 0.17 1.49 0.02

- 0.847 ( - 1.05)

-

0.065 (0.16) - 0.357

( - 1.61) 0.003

(0.92) -

0.429 (2.28) 0.098

(0.23) - -

- 0.024 ( - 1.23)

- 0.017 ( - 0.82)

- 0.013 ( - 1.21)

0.484 (2.95) 0.53 1.58(a) 0.02

- 1.208 ( - 2.52) -

0.741 (1.37)

- 0.539 ( - 3.40) - 0.003

( - 0.50) 0.014

(1.26) 0.634

(4.33) - 0.507

( - 1.01) - 0.004

( - 0.81) 0.018

(1.69)

-0.051 ( - 2.62)

0.018 (0.59)

0.006 (0.43)

-

0.90 0.19(a) 0.02

I statistics are in brackets. (a) Durbin h statistic.

The root mean squared errors of the out-of- sample forecasts derived from the various exchange rate models are given in Table 2. For the forecast horizon of one quarter, the forward rate results in the lowest root mean squared error, although uncovered interest parity and the dynamic sticky price monetary model also improve on the random walk model. At the two-quarter forecast horizon, the ranking changes slightly with uncovered interest parity improving on the forward rate and the dynamic sticky price monetary model. Again, all three models improve on the random walk model. The forward rate was not available for subsequent forecast horizons. For the remaining forecast horizons of three quarters and four quarters, the

dynamic sticky price monetary model outperforms all other models, including the no-change extrapolation. In contrast to other studies, the static monetary models as well as the dynamic flexible price model obtain lower root mean squared errors than the random walk model a t these horizons. However, the ARIMA and purchasing power parity models consistently perform poorly relative to the random walk model. There are some indications that purchasing power parity may give better results relative to other models a t longer forecast horizons. This may provide tentative support for continued interest in purchasing power parity as a long-run relationship.

The mean errors and mean absolute errors of the

1986 EXCHANGE RATE FORECASTING 22 1

TABLE 2 Root Mean Squared Errors (a)

Model

Horizon (quarters)

Equation number I 2 3 4

Random walk 3.93 6.87 9.66 12.47 ARIMA 4.92 8.54 12.25 16.43 Purchasing power parity

-instantaneous @) (3) 14.77 17.06 18.71 17.91 -partial adjustment @) (6) 8.60 9.95 11.15 12.46

Foward rate (8) 2.78 5.62 na na Uncovered interest parity (9) 2.98 4.86 na na Static monetary model

-flexible prices @) (14) 6.00 7.36 8.76 9.83 -sticky prices @) (20) 5.95 7.34 8.63 9.79

-sticky prices (c) (25) 3.75 5.92 7.65 8.92

Dynamic monetary model -flexible prices @) (23) 5.12 7.31 9.20 10.50

na-not available. (a) Approximately in percentage terms. @) Estimated using a Cochrane-Orcutt procedure to correct for first-order serial correlation. (c) Estimated by OLS.

forecasts are presenred in Tables 3 and 4, respectively. The lowest mean errors are obtained, at all forecast horizons, from the dynamic sticky price monetary model. The mean errors of the forecasts generated from the ARIMA model, the forward rate and uncovered interest parity are also lower than the mean errors obtained from the random walk model. For each of these models, the mean absolute error is considerably larger than the absolute value of the corresponding mean errors, indicating there is no consistent bias in the predictions. However, the remaining models do appear consistently to under-predict the exchange rate.

V Conclusion Structural and time-series models were compared

on the basis of their accuracy in forecasting the Australian-US dollar exchange rate out-of-sample. The forward rate was found to give superior forecasts at a horizon of one quarter. This would imply that, despite any alleged ‘thinness’ in the Australian forward exchange market, speculation brings the forward rate more into line with the actual future spot rate than other exchange rate forecasts. One criticism of using the forward rate as a predictor of the spot rate is that it gives little insight into the process of exchange rate determination. However, since the objective of this paper is t o compare exchange rate forecasts, this

point is of little immediate concern. In the structural models, mis-specification appears to be a general problem, given the presence of serially correlated errors in the estimated equations. At the two-quarter forecasting horizon, uncovered interest parity - a combination of arbitrage and speculation in foreign exchange markets - is the preferred model. For the remaining forecast horizons the dynamic specification of the sticky price monetary model outperformed all other models, including the random walk model.

Overall, the results of the current study are encouraging in that they lend support for continued efforts to model exchange rates. This contrasts with the work of Meese and Rogoff (1983). who found that estimated models failed to forecast better than the random walk model. However, they offered a number of possible explanations for their results, including sampling error, simultaneous equations bias, structural instability and mis-specification of the money demand functions. Of these, only the lattermost point has been explored in this paper.’ Further research on exchange rate modelling seems warranted, perhaps taking into account some of these other aspects.

7 Meese and Rogoff used monthly observations in their study. However, further (unreported) raults indicate that the relative forecasting performances of the competing models in this paper are similar whether monthly or quarterly data are used.


TABLE 3 Mean E R O ~ (a)

Horizon (quarters)

Model Equation number 1 2 3 4

~

Random walk ARIMA Purchasing power parity

-instantaneous (b) -partial adjustment (b)

Forward rate Uncovered interest party Static monetary model

-flexible prices (b) -sticky prices (b)

-flexible prices (b) -sticky prices (c)

Dynamic monetary model

-2.14 - 1.31

5.42 - 7.71 - 1.06

1.57

- 4.57 - 4.57

- 3.06 -0.15

- 4.42 - 2.16

4.53 - 8.79 - 2.52 - 0.69

- 5.95 - 6.08

- 4.43 - 0.34

- 6.88 - 2.46

3.13 - 9.80

na na

- 7.26 - 7.32

- 5.72 0.31

- 9.92 - 3.72

- 1.33 - 11.10

na na

- 8.32 - 8.47

- 7.20 0.98

na-not available. (a) Approximately in percentage terms. (b) Estimated using a Cochrane-Orcutt procedure to correct for first-order serial correlation. (c) Estimated by OLS.

TABLE 4 Mean Absolute Errors (a)

Horizon (quarters)

Model Equation number I 2 3 4

Random walk 3.23 6.27 8.79 10.73 ARIMA 3.79 6.80 9.25 13.45 Purchasing power parity

-instantaneous (b) (3) 10.00 12.07 14.73 15.06 -partial adjustment (b) (6) 7.71 8.79 10.1 I 11.10

Forward rate (8) 2.33 4.90 na na Uncovered interest parity (9) 2.42 4.20 na na Static monetary model

-flexible prica (b) (14) 5.22 6.38 7.78 8.32 -sticky prices @) (20) 5.25 6.48 7.76 8.47

-flexible prices (b) (23) 4.16 6.64 8.74 9.20 -sticky prices (c) (25) 3.13 5.12 6.70 8.23

Dynamic monetary model

na-not available. (a) Approximately in percentage terms. (b) Estimated using a Cochrane-Orcutt procedure to correct for first-order serial correlation. (c) Estimated by OLS.

REFERENCES Adam, C. M. (1983), Testing Monetary Models of the Baillie, R. T., Lippens, R. E. and McMahon, P. C.

Australian-US Exchange Rate’, Working Paper 83-010, (1983), Testing Rational Expectations and Efficiency Australian Graduate School of Management, in the Foreign Exchange Market’, Economefrica, 51, University of New South Wales. 553-63.


Bilson, J. F. 0. (1978). ‘Rational Expectations and the Exchange Rate’, in J. Frenkel and H. Johnson (eds), The Economics of Exchange Rates, Addison-Wesley Press, Reading.

Dombusch, R. (1976), ‘Expectations and Exchange Rate Dynamics’, JournalofPolitical Economy, 84, 1161-76.

Frankel, J. A. (1979a), T h e Diversifiability of Exchange Risk’, Journal of International Economics, 9,379-93.

+1979b), ‘On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Differentials’, American Economic Review, 69, 610-22.

- - (1982) , ‘The Mystery of the Multiplying Marks: A Modification of the Monetary Model’, Review of Economics and Statistics, 64, 515-19.

Frenkel, J. A. (1976), ‘A Monetary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence’, Scandinavian Journal of Economics, 78, 200-24.

-1981). ‘The Collapse of Purchasing Power Parities During the 1970s’. European Economic Review, 16, 14545.

---and Levich, R. M. (1979, r“Covered Interest Arbitrage: Unexploited Profits?’, Journal of Political Economy, 83, 325-38.

Hansen, L. P. and Hodrick. R. J. (1980), ‘Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric knalysis’, Journal of Political Economy, 88, 829-53.

Hogan, L. I., Urban, P. J. and Anh, V. V. (1985), ‘A

Vector Autoregressive Forecasting Model of the USS/SA Exchange Rate’, forthcoming in Australian Journal of Management.

Isard, P. (1978), ‘Exchange-Rate Determination: A Survey of Popular Views and Recent Models’, Princeton Studies in International Finance, No. 42, Princeton University.

M e , R. A. and Rogoff, K. (1983). ‘Empirical Ewchange Rate Models of the Seventies: Do They Fit Out of Sample?’, Journal of International Economics, 14,

Officer, L. H. (1976). ‘The Purchasing-Power-Parity Theory of Exchange Rates: A Review Article’, ZMF Staff Papers, 23, 1-60.

-1978). ‘The Relationship between Absolute and Relative Purchasing Power Parity’, Review of Economics and Statistics, 60, 562-8.

Pagan, A. R. and Volker, P. A. (1981), ‘The Short-run Demand for Transactions Balances in Australia’, Econornica, 48. 381-95.

Poole, W. (1967). ‘Speculative Prices as Random Walks: An Analysis of Ten Times Series of Flexible Exchange Rates’, Southern Economic Journal. 33,

Sims, C. A. (1974), ‘Seasonality in Regression’, Journal of the American Statistical Association, 69, 618-26.

Turnovsky, S. J. and Ball, K. M. (1983), ‘Covered Interest Parity and Speculative Efficiency: Some Empirical Evidence for Australia’. Economic Record, 59,271-80.

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a comparison of alternative exchange rate forecasting models

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