Is the Malaysian Foreign Exchange Market Efficient?

Dr. Omar Marashdeh

Senior Lecturer

Graduate School of Business

The University of Sydney

Locked Bag 20

Newtown, NSW 2042, Australia

E-mail: omarm@gsb.usyd.edu.au

Paper prepared for presentation at The Tenth Annual Australasian Finance & Banking Conference, 4-5 December 1997, Sydney, Australia,, and the Second Asian Academy of Management Conference, 12-13 December 1997, Langkawi, Kedah, Malaysia..

Abstract

This paper examines the Malaysian foreign exchange market efficiency for the USD, Singapore dollar, pound, and yen over the 1980:1-1994:12 period by utilizing Johansen-Juselius (JJ) Maximum Likelihood procedure. The bivariate cointegration results show the absence of cointegration among the bilateral exchange rates. This is further confirmed by the multivariate cointegration results which indicate the absence of a cointegration relationship among the four exchange rates. Thus, the foreign exchange markets for the four currencies are weakly efficient. However, these results were susceptible to the sample period under consideration. The subperiod analysis shows that a cointegrating relationship existed among the four currencies during 1980:1-1985:10 period. However, this relationship disappeared during the 1985:10-1994:12 period. Moreover, the results of the analysis remained the same after extending the sample to 1996:1. This implies that the Malaysian Foreign exchange market is weakly efficient.

1. Introduction

The efficiency of the foreign exchange markets has been examined by, among others, MacDonald and Taylor (1989), Levich (1989), Baillie and Bollerslev (1989), Coleman (1990), Copeland (1991), Tronzano (1992), Alexander and Johnson (1992), Masih and Masih (1994), Karfakis and Parikh (1994), and Baharumshah and Habibullah (1995). All of these studies with the exception of Baharumshah and Habibullah (who examined the Malaysian case) (1995) have examined the efficiency of foreign exchange markets in developed countries. Most of these studies, however, have used Engle and Granger two steps cointegration analysis in their approach to examining market efficiency with the exception of Baillie and Bollerslev (1989) and Karfakis and Parikh (1994) who use Johansen-Juselius (JJ) maximum likelihood procedure. In general, the Engle and Granger bivariate cointegration analysis leads to acceptance of the efficiency of the foreign exchange market, whereas the Johansen and Juselius multivaraite cointegration analysis, which accounts for interdependence among the exchange rates, leads to a rejection of the efficiency of the foreign exchange markets.

Baillie and Bollerslev (1989) test the efficiency of the U.S. daily spot and forward foreign exchange markets for seven currencies, namely, the pound, yen, mark, Canadian dollar, Italian lira, French franc, and the Swiss franc. They find that at least one common unit root is present in the seven daily spot and forward exchange rates. They conclude that the foreign exchange market is inefficient and the exchange rates are tied together by one long-run relationship.

Karfakis and Parikh (1994) examine the market efficiency of five major exchange rates of the Australian dollar by using Johansen and Juselius (1991) multivariate cointegration technique. They conclude that cointegrated relationships exist in the foreign exchange market when interdependence among exchange rates is accounted for.

Baharumshah and Habibullah (1995) examine the efficiency of the Malaysian foreign exchange market for six currencies, namely, the Malaysian ringgit (RM), Pound sterling, Deutsche mark, Japanese yen, Singapore dollar, and Swiss franc over the 1973:1-1992:8 period. In their study, the exchange rates were expressed as foreign currency per unit of US dollar. The closing prices at the end of the month/quarter were used. By using Engle and Granger bivariate cointegration technique, they find that the Malaysian spot exchange market is weakly efficient in the long-run. However, their results were sensitive to the sample period.

The purpose of this study is to test the efficiency of the Malaysian foreign exchange market for four major currencies, namely, the US dollar, the Japanese yen, the Singaporean dollar (SGD), and the British pound over the 1980:1-1994:12 period. The data are the average monthly Malaysian ringgit per unit of foreign currency. The data are obtained from Bank Division, Bank Negara Malaysia (BNM).

This study differs from Baharumshah and Habihullah (1995) in two aspects: 1) they use Engle and Granger bivariate cointegration analysis, whereas this study uses Johansen-Juselius multivariate cointegration analysis; and 2) their sample runs from 1973:1-1992:8, whereas this study uses more recent data from 1980:1 to 1994:12 and a hold out sample until 1996:1.

2. The Malaysian Foreign Exchange Market

Prior to 1972, the ringgit was linked to the sterling. The Malaysian ringgit severed its ties with the sterling on June 24, 1972 due to economic problems. The link to the U.S. dollar was established on June 24, 1972. On June 21, 1973, the ringgit was allowed to float. Since September 27, 1975, the ringgit has been determined by a weighted average of the major trading partners' currencies. However, neither the weight nor the currencies involved are known as the central bank does not divulge such information. The four countries in this study (Japan, UK, USA, and Singapore) accounted for 62% of total trade with Malaysia over the 1991-1993 period (Marashdeh (1995)).

The foreign exchange market has expanded since 1975. The monthly turn-over has increased from RM2 billion in 1975 to RM8.7 billion in 1985, RM37 billion in 1993, and 47.3 billion in 1994 (BNM, 1994a,b). In 1994, the U.S. dollar accounted for 62.8% of total transactions followed by the Deutsche mark (19%) and the Japanese yen (14.3%) (BNM, 1994b). The central bank intervened in the foreign exchange market to smooth the day to day fluctuations in the value of the ringgit (BNM, 1994). Such intervention was made heavily in the foreign exchange market in 1989, 1992 and 1994 to reduce the short-term/speculative flows to the Malaysian market which took advantage of the interest rate differentials between Malaysia and their home countries. The intervention took the form of restriction on swaps, limits on ringgit borrowing of commercial banks from offshore companies, limits on non-trade related external liabilities of banking institutions, revision of eligible liabilities base for computation of statutory reserve requirement and liquidity, prohibition of sale of short-term monetary instruments to non-residents, and placement of foreign vestro accounts with the central bank (BNM, 1994a,b).

The major players in the Malaysian foreign exchange market are all commercial banks, finance companies, and money-changers.

3. Methodology

The time series properties of the data are tested for stationarity by augmented Dickey-Fuller (ADF) test (due to Dickey and Fuller (1981)) and Phillips-Perron (PP) test (due to Phillips (1987), Phillips and Perron (1988) and Perron (1988)). The Dickey-Fuller test is based on the following equation for the jth exchange rate

Y_j,t = +Y_j,t-1 +Y_j,t-i +e_t (i=1,2,...,k) (1)

And the Phillips-Perron test is based on the following equation for the jth exchange rate

Y_j,t = +(1-)Y_j,t-1 + Y_j,t-i +v_t (i=1,2,...,k) (2)

Where j= USD, SGD, Pound, Yen. Y is the exchange rate, e and v are residual vectors.

A rejection of the unit root hypothesis implies that the exchange rate is stationary, i.e., integrated of order zero, I(0). Sufficient number of lags are included based on the highest significant autocorrelation function (ACF) and the partial autocorrelation function (PACF) to ensure that the residuals are not serially correlated.

The unit root tests are also performed on the first difference of the exchange rates to test for higher order unit roots. A rejection of the unit root hypothesis for the first difference means that the exchange rate is integrated of order one, i.e., I(1), and the first difference is integrated of order zero, I(0). That is, differencing the exchange rates once leads to stationarity.

The above equations are, also, augmented with a time trend to allow for the possible presence of deterministic time trend.

To examine whether a structural break in the series leads to the rejection of stationarity of the data in level form, Perron (1989) test for unit roots with structural change is applied. The test takes the form:

y_t = +t +DU +d(DTB) +y_t-1 + c_iy_t-i (i= 1,2,...k) (3)

where t is a time trend; DTB=1 for 1985:11 and zero otherwise; DU is a dummy variable which takes a value of 1 for t > 1985:10 and zero otherwise; measures the exogenous change in the rate of growth of the series; and d measures the exogenous change in the level of the series (see Perron 1989 for a discussion of the properties of the test).

Perron (1989) shows that under the unit root hypothesis: =0,

=0, =0, d=0, and =1, whereas under the alternative hypothesis of stationary fluctuations around a deterministic breaking trend function: 0, 0, 0, d=0, and <1. The optimal number of lags (k) is chosen based on the highest significant lag from the ACF or PACF functions.

The efficiency hypothesis test proceeds with Johansen and Juselius (1990 and 1992) Maximum Likelihood procedure which tests for the dependance of the exchange rates on each other. The procedure is based on the interim multiplier form of the vector autoregressive (VAR) representation of the system (equation (4)).

Y_t = _iY_t-i + _qY_t-q + _t+V_t (i=1,...,q-1) (4)

where Y_t is nx1 vector of exchange rates (Yen, SGD, USD, and Pound), _q is a square nxn matrix of ranks r n, is nx1 vector of constants and V_t is nx1 vector of residuals.

The testing procedure involves the null hypothesis H₀: _q=', i.e., there are at most r cointegrated vectors ₁, ₂,.., _r which provide r stationary linear combinations 'Y_t-q. The test proceeds by regressing the n-element vectors Y_t and Y_t-q on

Y_t-i, i=1,2,...,q-1, and monthly dummies, and obtaining the associated n-element residual vectors R₀(t) and R_q(t). The test for the number of cointegrating vectors is obtained by solving the eigenvalue problem

(5)

by the Choleski decomposition of S_qq. Where ,

i,j=0,q and T denotes the number of observations.

The Trace test, for the number of cointegrating vectors is less than or equal to r, _q=', is

-2ln(Q:H₂H₁)=- T Ln(1- _i) (i=r+1 to n) (6)

where _i corresponds to the n-r smallest eigenvalues of

S_q0S^-1₀₀S_0q with respect to S_qq. The maximal eigenvalue statistic for testing the null hypothesis that the number of cointegrating vectors is r (H₂(r)) against the alternative r+1 (H₂(r+1)) is given by

-2Ln(Q:rr+1) = - TLn(1- _r+1) (7)

The likelihood ratio test statistic of zero loading factors H4: =A in H2 is given by

-2ln(Q:H₄H₂) = T Ln{(1- _4,i)/(1- _i)} (i=1 to n) (8)

This is a test of weak exogeneity on the parameters of the matrix (Johansen and Juselius (1992)). That is, the loading factor _j (j=USD, SGD, Yen, Pound) entering the jth equation serves as a test of weak exogeneity of Y_j with respect to the cointegration vector.

The strong form of market efficiency says that in an efficient market the price of an asset should reflect all available information (Fama (1970 and 1991)). A weaker form of this hypothesis says that in an efficient market, the price should reflect all available information up to the point where the marginal cost of obtaining that information is equal to the marginal cost (Fama (1991)). On the other hand, the weak form of the market efficiency says that in an efficient market, the price of an asset should reflect all information which are contained in the past prices of the asset. The cointegration hypothesis says that if two exchange rates are cointegrated then one could be used to predict the other, i.e., evidence against market efficiency. Therefore, a rejection of the cointegration hypothesis leads to a rejection of the market efficiency hypothesis in favor of the error correction mechanism (ECM). Under ECM, past equilibrium errors could be used to predict current rates. Thus, a rejection of foreign exchange efficiency means that traders can use simple rules to out-perform the market.

4. Sensitivity Analysis

Earlier studies have shown that the results of Johansen-Juselius procedure is sensitive to model specifications and sample periods. With regard to model specifications, test is conducted for both bivariate and multivariate specifications for the exchange rates. With regard to sample size, the sample is further subdivided into two samples: 1980:1-1985:10 (prior to the intervention of the G-5 in the foreign exchange market) and 1985:10-1994:12 (post intervention). For stability of the results, both bivariate and multivariate specifications as well as the subsample results are expected to remain the same. Cheung and Lai (1993) state that the JJ method tends to over-estimate the number of cointegrating vectors when there are small samples with too many variables or lags. As such, this paper places more emphasis on higher confidence levels, say, 99% instead of the 95%, when using the trace and the maximal-eigenvalue test statistics.

To identify any period of temporal instability in the model, iterative tests for the number of cointegrating relationship, r, are conducted. The test proceeds from an initial estimate of the subsample 1980:1-1985:10 and successively proceeds by iterating r until the end of the period. The test was further extended beyond the sample period to 1996:1 to examine the stability of the results after 1994:12.

5. Empirical Results

Table 1 shows the augmented Dickey-Fuller and Phillips-Perron tests for unit roots in the four exchange rates. The table shows that all exchange rates in their level form are I(1) while in first difference are I(0), i.e., the exchange rates become stationary after differencing once.

Insert table 1 here

These results are further confirmed by the Perron test for structural break after the agreement of the Finance Ministers of the G-5 to intervene in the foreign exchange market to adjust the US dollar exchange rate. The test shows that all series displays a unit root in their level form.

Insert table 2 here

Table 3 shows the Johansen-Juselius maximum likelihood bivariate test for the efficiency of the exchange market. The test covers 1980:1-1994:12; 1980:1-1985:10; and 1985:10-1994:12 periods for the six bilateral combinations of the exchange rates. The lag length was determined based on minimization of Akaike final prediction error (FPE) and serial correlations. For the 1980:1-1994:12 period, the table shows that the hypothesis of at least 2 stochastic trends in all bilateral exchange rates could not be rejected. That is, the bilateral exchange markets are weakly efficient. For the 1980:1-1985:10 period, however, the table shows that the foreign exchange market is weakly efficient except for the SGD-Yen and SGD-USD markets. For the 1985:10-1994:12 period, the foreign exchange market is weakly efficient as the cointegration hypothesis was accepted for all bilateral combinations of the exchange rates.

Insert table 3 here

The lag length in the multivariate cointegrating system is determined by minimization of the FPE and tests for normality and serial correlation in the residuals for each equation. The optimal number of lags to remove serial correlations form the systems is achieved at 6 lags, but no lag length is able to ensure that all residuals pass normality test. At lags less than 6, the system suffers from serial autocorrelations. The results for the model with 7 or 5 lags are similar to the models with 6 lags. Therefore, the results reported in this paper are for the models with 6 lags.

Table 4 shows the residual misspecification tests for the VAR models for the whole sample and the two subsamples. For the whole sample, the table shows that the Yen, SGD, and USD equations suffer from excess skewness while the Yen, SGD, USD, and Pound equations suffer from excess kurtosis. Jarque-Bera test shows that the residual vectors for the four equations deviate significantly from normality. For the 1980:1-1985:10 period, the table shows that the residual vectors do not deviate from normality. However, for 1985:10-1994:12 period, the residual vectors exhibit significant skewness, kurtosis, and deviate significantly from normality. Johansen-Juselius (1992) indicate that deviation from normality may not bias the results as long as the errors admit a central limit theorem.

Insert table 4 here

Table 5 shows the results of applying Johansen-Juselius maximum likelihood cointegration test for the VAR models for the three periods: 1980:1-1994:12; 1980:1-1985:10; and 1985:10-1994:12. For the whole period, the maximal eigenvalue and trace tests show that the hypothesis of at least 4 stochastic trends in the four equations system which determines the spot rates could not be rejected, i.e., the foreign exchange market is weakly efficient. However, this conclusion is susceptible to the sample period. For the 1980:1-1985:10 period, the maximal eigenvalue and trace tests confirm the presence of three stochastic trends in the four equation model, or one long-run relationship among the four exchange rates. That is, a common I(0) disequilibrium error among the four currencies partly determines the monthly changes in the exchange rates for the 1980:1-1985:10 period. This relationship may provide evidence against foreign exchange market efficiency during the 1980:1-1985:10. This finding collaborates the findings of Baillie and Bollerslev (1989) and Kurfakis and Parikh (1994).

However, this long-run relationship becomes less significant for the 1985:10-1994:12 period as the maximal eigenvalue test is statistically significant at the 10% only. These results show that the exchange market tends to be more efficient, the longer the time period under considerations as evident by the 1980:1-1994:12 and 1985:10-1994:12 periods against the 1980:1-1985:10 period. These findings confirm the findings of earlier studies (for example see Sephton and Larsen (1991)) that the JJ method is sensitive to model specifications and time period.

Insert table 5

To examine whether the cointegration relationship 'Y_t-q does not enter all equations of the VAR system for the 1980:1-1985:10 period, the likelihood ratio test (equation 8) is applied. The results of the likelihood ratio tests on the loading factors indicate that the null hypothesis of zero loading is rejected for all currencies (see table 6). This implies that the four currencies adjust to clear the non-equilibrium in the foreign exchange market.

Insert table 6 here

The results of the iterative Johansen-Juselius test for the temporal stability of the results are presented in table 7. The table shows that instability of the results took place only in October 1985. Thereafter, the results remained stable. However, these results are dependent on the starting date of the estimation period as evident by the results for the subsamples reported in table 5. After extending the sample period to 1996:1 and conducting the JJ test, the results remained the same as those for the 1980:1-1994:12 sample. Thus, the long-run stability of the estimated results, based on 1980:1 starting date, are robust.

Insert Table 7 here

6. Conclusion

The purpose of this paper is to study the efficiency of the Malaysian Foreign exchange market for four currencies, namely, USD, SGD, Yen, and Pound over the 1980:1-1994:12 period. Johansen-Juselius maximum likelihood cointegration technique is employed in the analysis. The bivariate tests show that the foreign exchange market is weakly efficient. However, when the exchange rates interdependence is taken into account, the foreign exchange market is weakly efficient for the whole period. However, for the subperiod 1980:1-1985:10 the evidence indicates that at least one unit root exists among the four exchange rates, i.e., a long run relationship exists among the four exchange rates. The disequilibrium error from this relationship could be used to predict next period's exchange rate. This disequilibrium error provides evidence against weak form efficiency of the exchange rate. As for the subperiod 1985:10-1994:12, the foreign exchange market is weakly efficient. The bivariate JJ test for the subperiods confirms the findings for the multivariate JJ test.

JJ iterative tests indicate the presence of one cointegrating vector prior to 1985:10 and the absence of this cointegrating vector thereafter. Moreover, after extending the sample to 1996:1, the results remained the same as those for the 1980:1-1994:12 period. That is, in the long-run, the Malaysian foreign exchange market is weakly efficient. Inefficiencies in the foreign exchange market may take place in the short-run due to government interventions, thin trading and market imperfections. In the long-run, however, these inefficiencies are more likely to disappear. As such, the cointegration results across model specifications and time appear to be robust.

Caution should be exercised when using these results due to the limited scope of the technique employed and its sensitivity to starting date, sample size and number of lags employed. In case where evidence was suggestive of market inefficiency, it is possible that transaction costs could eliminate this inefficiency in the market.

7. References

Alexander, C.O. and A. Johnson, (1992), Are foreign exchange markets really efficient?, Economics Letters 40, 449-453.

Baharumshah A.Z. and M.S. Habibullah, (1995), The efficiency of the spot foreign exchange market: evidence from the Malaysian currency market, paper presented at the Third Malaysian Econometric Conference, June 14-15, Kuala Lumpur, Malaysia.

Baillie Richard T. and Tim Bollerslev, (1989), Common stochastic trends in a system of exchange rates, The Journal of Finance XLIV, 167-181.

Bank Negara Malaysia (1994a), Money and Banking in Malaysia: 35th Anniversary Edition 1959-1994, Kuala Lumpur, Malaysia.

--------- (1994b), Annual Report 1994, Kuala Lumpur, Malaysia.

Cheung, Y.W. and Lai, K.S (1993), Finite-sample sizes of Johansen's likelihood ratio test for cointegration, Oxford Bulletin of Economics and Statistics, 55 (3), 313-328.

Coleman, M, (1990), Cointegration-based test of daily foreign exchange market efficiency, Economic Letters 32, 53-59.

Copeland, L, (1991), Cointegration test of daily foreign exchange data, Oxford Bulletin of Economics and Statistics 53, 185-198.

Dickey, D.A. and Fuller, W.A, (1981), Likelihood ratio statistics for autoregressive time series with a unit root, Econometrica 49, 1057-72.

Engle, R. F. and Granger, C. W. J, (1987), Cointegration and the error correction: representation, estimation and testing, Econometrica 55, 251-76.

Fama, E.F, (1970), Efficient capital markets: review of theory and empirical work, Journal of Finance 25, 383-417.

---------, (1991), Efficient capital markets II, The Journal of Finance, XLVI, 1575-1617.

Johansen S. and K. Juselius, (1990), Maximum likelihood estimation and inference on cointegration-with application to Demand For Money, Oxford Bulletin of Economics and Statistics 52, 169-210.

------------(1992), Testing structural hypothesis in a multivariate cointegration analysis of the PPP and the UP for the UK, Journal of Econometrics, 53, 211-244.

Karfakis, Costas I. and Ashok Parikh (1994), Exchange rate convergence and market efficiency, Applied Financial Economics 4, 93-98.

Levich, R.M, (1989), Is the foreign exchange market efficient? Oxford Review of Economic Policy 5, 40-60.

MacDonald, R. and M.P. Taylor (1989), Foreign exchange market efficiency and cointegration: some evidence from recent float, Economics Letters 29, 63-68.

Marashdeh, O., (1995), The effect of the foreign exchange rate on the demand for financial assets in Malaysia, in M. Sulaiman, A.G. Shafie, and J.H. Ali (eds): Proceedings of the First Annual Asian Academy of Management Conference, Universiti Sains Malaysia, Penang, Malaysia, pp. 156-166.

Masih A. M.M. and Masih R, (1994), On the robustness of cointegration tests of the market efficiency hypothesis: evidence from six European foreign exchange markets, Economia Internazionale XLVII, 160-180.

Perron P. (1988), Trends and random walks in macroeconomic time series, Journal of Economic Dynamics and Control, 12, 297-332.

-------- (1989), The great crash, the oil price shock, and the unit root hypothesis, Econometrica, 57, 1361-1401.

Phillips P. (1987), Time series regression with a unit root, Econometrica, 55, 277-301.

Phillips P. and Perron P. (1988), Testing for a unit roots time series regression, Biometrika, 75, 335-346.

Phillips, P (1991), Unidentified components in reduced rank regression estimation of ECM's, Yale University, Mimo.

Sephton P.S. and Larsen H.K. (1991), Tests of exchange market efficiency: fragile evidence from cointegration tests, Journal of International Money and Finance, 10, 561-570.

Tronzano, M, (1992), efficiency in German and Japanese foreign exchange markets: evidence from cointegration techniques, Review of World Economics 128, 1-20.

Table 1

Tests of the Unit Roots hypothesis for the Exchange Rates (1980:1-1994:12)

Currency No Trend Trend

ADF(_u) Z() Z(t) Z(₁) ADF() Z(*) Z(t_*) Z(₂) Z(₃) Lag

Level Form

Yen -0.56 -0.21 -0.15 2.42 -3.19+ -8.67 -2.15 3.21 2.49 11

SGD 0.78 0.64 0.65 5.68+ -1.44 -6.49 -1.83 5.05+ 2.38 7

Pound -2.12 -5.52 -1.77 1.68 -2.29 -5.63 -1.81 1.25 1.76 8

USD -2.04 -4.65 -1.92 2.26 -1.01 -8.45 -1.90 1.82 2.36 11

First Difference

Yen -3.03+ -131.6* -10.1* 50.96* -3.06+ -130.4* -10.05* 33.71* 50.55* 13

SGD -3.49* -104.13* -10.01* 49.87* -3.75* -101.46* -10.06* 33.44* 50.16* 11

Pound -4.49* -100.72* -8.88* 39.33* -4.10* -100.45* -8.86* 26.07* 39.09* 7

USD -3.62* -100.78* -10.71* 56.97* -3.76* -97.45* -10.83* 38.62* 57.93* 13

* Significant at the 1% level. + Significant at the 5% level.

The order of lags is set as the highest significant lag order from either the ACF or PACF of the first difference series.

ADF(_u) and ADF() are the augmented Dickey-Fuller test for =0 in the no trend and trend cases, respectively.

Z() and Z(*) are Phillips' (1987) tests for =1 in the no trend and trend cases, respectively. Z(t) and Z(t_*) are the Phillips-Perron's (1988) tests for =1 in the no trend and trend cases, respectively.

Z(₁) is the Phillips-Perron test for =0 and =1 in the no trend case.

Z(₂) is the Phillips-Perron test for *=*=0 and *=1 in the trend case.

Z(₃) is the Phillips-Perron test for =0 and *=1 in the trend case.

Table 2

Perron Tests for Structural Change in October, 1985

y= +t+DU+dDTB+y_t-1+ c_iy_t-i (i= 1,2,...k)

Currency t t t d t_d t lag lambda R

Yen 0.051 3.20 0.036 2.60 0.0004 2.22 0.039 0.89 0.931 -3.18 10 0.38 0.995

Pound 0.159 2.53 0.085 2.27 -0.0004 -1.4 -0.101 -0.92 0.957 -2.85 8 0.38 0.971 USD 0.158 1.86 0.017 1.47 -0.0001 -0.4 0.035 1.1 0.936 -1.71 11 0.38 0.965

SGD 0.023 1.16 0.004 0.71 0.0001 0.81 -0.020 -1.3 0.978 -1.03 7 0.38 0.996

The test is for =0, =0, =0, d=0, and =1.

The level of significance for =1 and lambda= 0.4 is -4.34 at the 1% level and -3.72 at the 5% level (Perron 1989, Table IV.B, p. 1376).

Lambda is time of break relative to sample size.

Table 3

Bivariate Johansen Tests between alternative Currencies

Relationship	Lag	H0: r=0		H0: r=1
		Trace	Maximal Eigenvalue	Maximal Eigenvalue & Trace
1980:1-1994:12 Period
Pound-USD	11	18.539	14.104	4.436
Pound-SGD	8	7.491	7.081	0.410
SGD-Yen	11	8.644	8.557	0.086
SGD-USD	11	13.647	13.641	0.006
USD-Yen	11	7.304	6.278	1.026
Yen-Pound	11	12.245	11.065	1.181
1980:1-1985:10 Period
Pound-USD	11	13.3	10.861	2.439
Pound-SGD	8	6.3	4.766	1.534
SGD-Yen	11	17.639	16.929**	0.71
SGD-USD	11	19.907	18.884*	1.023
USD-Yen	11	19.597	14.684	4.911
Yen-Pound	11	7.221	5.428	1.794
1985:10-1994:12 Period
Pound-USD	11	11.440	9.354	0.209
Pound-SGD	8	3.855	3.853	0.002
SGD-Yen	11	6.249	5.315	0.934
SGD-USD	11	11.394	11.391	0.003
USD-Yen	11	3.549	3.431	0.071
Yen-Pound	11	2.421	2.222	0.199

* and ** Significant at the 1% and 2.5% levels, respectively.

Table 4

Residual Misspecification Tests in the VAR Model

Equation	FPE	Q(20)	SK	KR	JB(2)	Sigma
1980:1-1994:12 Period
Yen	0.0023	29.84	0.664*	1.639*	30.20*	0.044
SGD	0.0003	20.15	0.293*	4.628*	146.78*	0.015
USD	0.0134	19.11	-0.565*	3.179*	76.72*	0.107
Pound	0.0011	29.63	0.229	4.279*	124.73*	0.031
1980:1-1985:10 Period
Yen	0.0006	12.28	0.472	-0.156	2.421	0.021
SGD	0.0001	15.28	0.213	-0.276	0.783	0.007
USD	0.0101	21.93	0.441	0.978	3.784	0.082
Pound	0.0015	15.41	-0.026	0.919	1.532	0.031
1985:10-1994:12 Period
Yen	0.01254	4.29	9.01*	104.0*	****	0.1029
SGD	0.01025	1.57	11.39*	143.7*	****	0.0930
USD	0.10381	2.74	10.17*	124.6*	****	0.2961
Pound	0.04673	1.45	11.54*	146.2*	****	0.1987

Sigma refers to the standard error of the equation.

Q(20) refer to Ljung-Box Q statistic for serial correlation for the first 20 autocorrelations.

JB= Jarque-Bera test for normality of residuals.

FPE refers to Akaike information criterion.

SK refers to skewness.

KR refers to kurtosis.

* Statistically significant at the 5% or better.

**** Statistically significant at the 1%.

Table 5

Johansen-Juselius maximum likelihood cointegration tests

r	n-r	Trace	Maximal eigenvalue	Eigenvalue
1980:1-1994:12 Period
0	4	37.724	17.639	0.0964
1	3	20.085	13.34	0.0738
2	2	6.745	6.015	0.03398
3	1	0.729	0.729	0.00418
1980:1-1985:10 Period
0	4	68.496*	41.283*	0.47537
1	3	27.213	16.758	0.23037
2	2	10.455	9.592	0.13919
3	1	0.863	0.863	0.01340
1985:10-1994:12 Period
0	4	44.693	26.819	0.14284
1	3	17.874	11.549	0.06422
2	2	6.325	6.260	0.03534
3	1	0.065	0.065	0.00037

* significant at the 1% levels.

r and n-r denote the number of eigenvectors and common trends, respectively.

Table 6

Testing for zero loading factors

-Restriction Eigenvalues -2lnQ(H₄\H₂)

1980:1-1985:10 Period

H₂: _q=' (0.47537 0.23037 0.13919 0.134)

H₄: _J=0 (0.26158 0.11826 0.03648 0.000) (1)=23.24*

H₄: _S=0 (0.20359 0.05317 0.00679 0.000) (1)=28.38*

H₄: _Uk=0 (0.35410 0.15710 0.00077 0.000) (1)=14.14*

H₄: _US=0 (0.16944 0.04998 0.00874 0.000) (1)=31.24*

* indicates significant at the 5%.

Table 7

Iterated Johansen-Juselius Test for the Four Exchange Rates System

Sample	H0: r=0 (n=4)		H0: r=1 (n=3)
	Maximal eigenvalue	Trace	Maximal eigenvalue	trace
1980:1-1985:10	41.283*	68.496*	16.758	27.213
1980:1-1986:10	17.737	38.109	13.351	20.372
1980:1-1987:10	22.108	41.76	11.501	19.742
1980:1-1988:10	19.977	35.992	8.391	16.015
1980:1-1989:10	21.71	38.45	9.72	16.741
1980:1-1990:10	20.611	40.745	12.627	20.134
1980:1-1991:10	20.144	38.17	11.738	18.027
1980:1-1992:10	15.502	30.982	10.869	15.481
1980:1-1993:10	20.139	40.227	13.418	20.088
1980:1-1994:12	17.639	37.724	13.34	20.085
1980:1-1996:1	15.636	35.772	13.351	20.136

* Significant at the 1% level. The significance levels for r=0 and r=1 at the 1% are 32.616 and 26.154 for maximal eigenvalue, respectively. The significance levels for r=0 and r=1 at the 1% for the trace are 55.551 and 37.291, respectively.