Efficiency tests of foreign exchange markets for four Asian Countries

Research in International Business and Finance 24 (2010) 284–294

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Research in International Business and Finance j o ur na l ho me pa ge : w w w . e l s e v i e r . c o m / l o c a t e / r i b a f

Efficiency tests of foreign exchange markets for four Asian Countries Shu-Mei Chiang a, Yen-Hsien Lee b,∗, Hsin-Mei Su c, Yi-Pin Tzou c a

Department of Finance, Lunghwa University of Science and Technology, 300, Sec. 1, Wanshou Rd., Guishan Shiang, Taoyuan County, Taiwan b Department of Finance, Chung Yuan Christian University, 200, Chung Pei Rd., Chung Li, Taoyuan County, Taiwan c Department of Banking and Finance, Tamkang University, 151, Ying-Chuan Rd., Danshuei Township, Taipei county, Taiwan

a r t i c l e

i n f o

Article history: Received 10 March 2008 Received in revised form 20 July 2009 Accepted 8 January 2010 Available online 11 February 2010 JEL classification: C22 G15 Keywords: Floating exchange rate Variance ratio test Multiple-variance ratio test Random walk

a b s t r a c t This paper uses the traditional variance ratio test of Lo and MacKinlay (1988, 1989), the non-parametric-based variance ratio test of Wright (2000) and the multiple-variance ratio test of Chow and Denning (1993), to re-examine the validity of the weak form efficient market hypothesis for foreign exchange markets in four floating-rate markets in neighboring Asian economies (Japan, South Korea, Taiwan and the Philippines). The results show that the random walk patterns of the exchange rate return series cannot be rejected, with the one exception of Taiwan, where inefficiency is shown to be most prominent. We therefore conclude that the foreign exchange markets of Japan, South Korea and the Philippines are weak form efficient, while the foreign exchange market of Taiwan is inefficient. © 2010 Published by Elsevier B.V.

1. Introduction There is an abundance of prior studies in which the behavior of asset prices has been examined. One method of testing for weak form market efficiency has been to determine whether the behavior of asset prices follows a random walk pattern; with the random walk hypothesis contending that consecutive price changes in an efficient market are irregular. However, if the series of asset prices exhibit mean reversion, then the prices are regarded as being serially correlated, and it is therefore feasible to forecast their behavior in the long run. Belaire-Franch and Opong (2002) noted that if asset returns could be modeled, this would suggest that stock returns may also be predicted. Clearly,

∗ Corresponding author. E-mail address: [email protected] (Y.-H. Lee). 0275-5319/$ – see front matter © 2010 Published by Elsevier B.V. doi:10.1016/j.ribaf.2010.01.001

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such information would be extremely valuable to investors, academics and regulators; consequently, an understanding of the behavior of asset prices and how empirically accurate, within the markets, the random walk hypothesis may be, are of considerable importance to a number of interrelated groups.1 A substantial number of academic studies have emerged over recent years in which advanced modeling techniques have been used to examine the behavior of financial markets (Liu and He, 1991; Lee and Ike, 1999; Wright, 2000; Belaire-Franch and Opong, 2005). Although, in the majority of these studies, the results have shown that financial markets are inefficient (with their price series usually exhibiting mean reversion), the findings on the weak form efficient market hypothesis generally remain inconclusive. Furthermore, only in a very few studies, of which we are aware, has there been any investigation of the efficiency of foreign exchange markets in Asian economies, particularly those with floating exchange rate systems.2 Within those studies where an investigation of market efficiency has been undertaken on emerging markets, the focus has generally been on the stock market (Darrat and Zong, 2000; Cheung and Coutts, 2001; Poshakwale, 2002; Worthington and Higgs, 2003; Lima and Tabak, 2004; Ainul and Mohammed, 2005; Füss, 2005; Hoque et al., 2007; Al-Khazali et al., 2007). In addition, some studies of exchange rate efficiency in the Australasian region are also debated recently. A general list of prior studies is presented in Table 1. The controversial and mixed results in the literature have referred to alternative testing methods, different data periods, and dissimilar frequencies of data (for example, Olekalns and Wilkins, 1998; Henry and Olekalns, 2002; Jeon and Seo, 2003; Oh et al., 2007; Sohel Azad, 2009). Thus, determining which financial market is more efficient is of importance when markets seem to exhibit the same efficiency or inefficiency levels under various tests. The purpose of this paper is therefore to contribute to this important topic by examining the behavior of four countries in Asia with floating exchange rates. A floating exchange rate, or a flexible exchange rate, is a type of exchange rate regime within which a currency’s value is allowed to fluctuate according to the foreign exchange market. Within such systems, it would be unusual for the central bank to frequently intervene to stabilize the currency. Consequently, in a country with a floating exchange rate system, the foreign exchange market should be efficient; that is, the foreign exchange rate series will exhibit a random walk pattern. What we aim to determine here, however, is what the situation is in reality. We examine this question with regard to four Asian economies, Japan, South Korea, Taiwan and the Philippines, with the foreign exchange markets in these countries providing us, for a number of reasons, with an excellent opportunity to study efficiency. First of all, their exchange rates are free floating, as defined and published by the International Monetary Fund (IMF). In particular, the foreign exchange markets are of exceptional importance to economic policy within these economies since they are all oriented towards export trade.3 In addition, Chen et al. (2006) point out that the movements of exchange rates have major impacts on foreign direct investments. Specifically, after the Asian currency crisis, the impacts of capital flows, economic or uneconomic factors and exchange rate stabilization (Krongkaew, 1999; Ariff and Abubakar, 1999; Kunimune, 1999) on foreign exchange markets attract more mass population’s attention. Even more, the nearby currency crisis in Argentinean show that the exchange rate regime plays a significant role in economics (Alvarez-Plata and Schrooten, 2006). We can see, therefore, above results show that an efficient foreign exchange market is important. Secondly, with the exception of Japan, the greatest economic system of the four economies examined, the uncertainty stemming from non-economic impact on the foreign exchange markets (such as general elections, strikes, and so on) is also significant for these countries. Accordingly, their exchange

1 An efficient market generates prices that can fully reflect all available information (Fama, 1991); accordingly, asset returns are purely non-predictable and no investors can earn abnormal profits by exploiting past available information. The implication is therefore that prices traded in such a market will be serially uncorrelated. 2 Karfakis and Parikh (1994) examine the market efficiency hypothesis for five major exchange rates of the Australian dollar. Masih and Masih (1995) aim to examine Canadian floating dollar and six other major European currencies, in testing the market efficiency hypothesis (MEH) use cointegration techniques. 3 Although Japan possesses the highest foreign exchange reserves in the world, the ratios for South Korea, Taiwan and the Philippines are also between 60% and 104% (the (exports + imports)/GNP ratios are available upon request); which clearly indicates that the three Asian developing countries are also heavily dependent on the foreign exchange market.

Region

Summary

Kearney and MacDonald (1990)

Australia

Corbae and Ouliars (1991)

Australia

Kearney and MacDonald (1991)

Australia

Olekalns and Wilkins (1998)

Australia

Manzur and Pui (2001)

Australia and Singapore Australia

This paper examined the role of fundamental economic variable in explaining movements in the Australian/US dollar exchange rate during the period of floating rates. The results of tests are supportive of the model for reasonable ranges of the money demand elasticities, while indicating the absence of speculative bubbles during the float. This study used Engle and Granger (1987) theory of cointegrated processes to test the absolute version of PPP. The empirical results provide little support for the absolute version of PPP since the real effective exchange rate of Australia and its bilateral exchange rates are integrated processes. It follows that the real exchange rate are not mean-reverting. This paper examined the relationship which exists between the spot and forward Australian/US dollar exchange rate for one-, three- and six-month contracts over the period January 1984–March 1987. In accordance with the assertions of Mussa (1979), the change in the spot exchange rate does not follow a random walk while the forecast errors also exhibit autocorrelation. This paper re-examined the same Australian data set analyzed by Corbae and Ouliars (1991) by calculating non-parametric measures of persistence and estimating fractionally integrated ARMA models. It finds evidence that Australia’s real exchange rate displays long run mean reversion, although there are some indications that PPP broke down during the inter-war period. This paper examined some key issues including PPP, IRP and EMH in the Australia and Singapore foreign exchange markets. Results lend strong support to unbiased efficiency in the bilateral exchange rates for these two economies. This paper tested an Australian quarterly real trade weighted index for evidence of mean reversion. A wide range of parametric and semi-parametric estimators were employed in an effort to obtain inferences that are robust to problems associated with non-stationary data. There was little consistent evidence of mean reversion in the data. This paper investigated whether the Asian financial crisis in the second half of 1997 affected the foreign exchange market efficiency in four Asian countries hit hard by the crisis: Thailand, Indonesia, Malaysia and Korea. The empirical evidence is mostly consistent with the across-country efficient market hypothesis in the foreign exchange markets during the whole sample period except the short period immediately after the July1997 crisis. The paper studied the PPP in Australia using an alternative method relative to previous studies. Once it adjusted the data of these outliers that had large, but either temporary or permanent effects on the series, the results show that there is no tendency for PPP in Australia to hold in the long run during this period. This study provides an application of the efficient exchange market hypothesis to the case of a number of post-crisis Asia-Pacific countries namely Korea, Taiwan, Thailand, Indonesia, Malaysia, Philippines, Japan, Singapore, Australia and New Zealand. The evidence obtained from the across-country study, cointegration tests were performed in order to re-examine within-country co-movements between forward and future spot exchange rates. The test results generally support the market efficiency hypothesis. In this paper, we have investigated the degree of randomness in the time series of 17 foreign exchange markets. We employed the Apron to quantify market efficiency in the foreign exchange markets. We found that the efficiency of markets with a small liquidity such as Asian foreign exchange markets improved significantly after the Asian currency crisis. This paper empirically tests the random walk and efficiency hypothesis for 12 Asia-Pacific foreign exchange markets. With the daily data, unit root tests identify unit root components for all the series and two variance ratio tests provide the evidence of martingale behavior for majority of the exchange rates tested. With the weekly data, only the variance ratio tests reject the martingale null for the majority of the exchange rates.

Henry and Olekalns (2002)

Jeon and Seo (2003)

Thailand, Indonesia, Malaysia and Korea

Darné and Hoarau (2007)

Australia

Kan and Andreosso-O’Callaghan (2007)

Asia and Australia

Oh et al. (2007)

European, North American, African, Asian and Pacific

Sohel Azad (2009)

Asia-Pacific

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Papers

286

Table 1 The studies of exchange market efficiency in Australasia: 1990–2009.

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rates are susceptible to fluctuation; hence, the reason for our examination of the efficiency of the foreign exchange markets for these developed and developing Asian economies. An understanding of efficiency within these four economies will not only help investors to appraise their risk, but it should also help them to devise adequate investment and hedging policies capable of responding to changes in the foreign exchange market. In those studies in which an examination of the random walk hypothesis was undertaken with regard to financial markets, variance ratio tests (Lo and MacKinlay, 1988, 1989) have been the most widely used design; however, the traditional tests do suffer from inherent limitations.4 According to Wright (2000), when testing the random walk hypothesis in foreign exchange markets, non-parametric-based tests (variance ratio tests with ranks and signs) are more effective than the traditional variance ratio test proposed by Lo and MacKinlay (1988, 1989). Nevertheless, since the results of both the Lo and MacKinlay (1988, 1989) and Wright (2000) tests tend to provide inconsistent conclusions for different sampling periods, we adopt the multiplevariance ratio test of Chow and Denning (1993) to adjust the individual variance ratio tests during a specific interval, so as to cover all possible intervals, a method more in accordance with the random walk hypothesis. We therefore apply the traditional variance ratio test to initially assess efficiency within the four Asian floating exchange rate economies. Thereafter, in order to ensure a thorough comparison of efficiency levels, we apply the non-parametric-based and multiple-variance ratio tests to examine the behavior of the foreign exchange rate series. When attempting to use the whole sample periods in our analysis, it is quite difficult to determine which periods are efficient or inefficient. Therefore, in order to avoid the uncertainty of ‘canceling out’ created by information in the long run, and so as to assess which foreign exchange market is comparatively efficient, we use a fixed-sized rolling window of 250 observations, applying both the non-parametric-based and variance ratio tests to compute and compare the ratio of efficiency for each country during the whole sample period. This study represents the first of its kind to undertake a comparison of efficiency levels by increasing the power of the tests amongst the four countries examined. The results demonstrate that of these four Asian economies, Taiwan is the most inefficient. As regards the foreign exchange markets of Japan, South Korea and the Philippines, the same conclusion is drawn from all three testing methods, that they are weak form efficient. We surmise that in an attempt to maintain economic development and stability in the financial market, the government and the central bank in Taiwan are regularly intervening in the foreign exchange markets. The remainder of this paper is organized as follows. Section 2 describes the data and empirical results. The conclusions drawn from the study are presented in Section 3. Finally, the appendix illustrates the derivations of empirical methodology adopted for this study. 2. Data and estimation results 2.1. Data In our examination of whether the related foreign exchange markets are efficient, we utilize the daily foreign exchange rate closing prices of Japan, South Korea, Taiwan and the Philippines obtained from the AREMOS database. The foreign exchange rates of the four Asian economies are all floating, as defined and published by the IMF. The sample period for this study runs from 1 January 1998 to 23 Augusts 2006, a period which provides a total of 2256 observations. All foreign exchange rates are logarithms of the nominal foreign exchange rates, with all of the analyses being conducted on returns data. The sample foreign exchange rates are defined as follows: LY = ln(Y )

4

Detailed descriptions are provided in Worthington and Higgs (2003) and Al-Khazali et al. (2007).

(1)

288

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Table 2 Descriptive statistics of daily exchange rates. Country LJPY LKRW LTWD LPHP a b ***

Mean 4.7555 7.0708 3.4985 3.8878

Std. dev. 0.0769 0.1087 0.0386 0.1341

Skewness ***

0.5504 0.2370*** −0.2593*** −0.7065***

Kurtosisa

Max.

Min.

Jarque-Bera testb

−0.1309 0.8806*** −1.0066*** −1.0770***

4.6196 6.8328 3.4115 3.6096

4.9922 7.5011 3.5608 4.0335

115.4510*** 93.9684*** 120.3623*** 296.5907***

Kurtosis is the excess kurtosis. Refers to the Jarque-Bera normal distribution test. Indicates significance at the 1% level.

where Y = JPY, KRW, TWD and PHP, JPY refers to the Japanese Yen, KRW refers to the South Korean Won, TWD refers to the Taiwan Dollar and PHP refers to the Philippines Peso; all are in relation to the US dollar. 2.2. Preliminary analysis In this paper, we apply the traditional variance ratio test and then go on to use the non-parametricbased test of Wright (2000) and the multiple-variance ratio test of Chow and Denning (1993) to examine the behavior of the foreign exchange rate series for the four Asian economies. The derivations of testing methods are interpreted in Appendix. Table 2 presents the summary statistics of the daily exchange rate returns for the exchange markets of the four countries, with the return series of the four markets exhibiting significant levels of skewness and kurtosis. We find that skewness is positive for both Japan and South Korea, indicating that, as compared to normal distribution, the exchange rate returns are flatter to the right; conversely, the returns for Taiwan and the Philippines are flatter to the left. With regard to the excess kurtosis, three of the four markets were significantly different from zero, the one exception being Japan. The Jarque–Bera tests for normality were all significant. These characteristics demonstrate that exchange rate distribution is not normal, and that this is attributable to intertemporal dependence amongst the serial momentums. 2.3. Empirical results 2.3.1. The variance ratio tests The estimates of the variance ratio tests, the variance ratio tests on ranks and signs and the multiplevariance ratios for the four economies examined are presented in Table 3, along with the associated test statistics for lags k = 2, 5, 10, 15 and 20, for the entire sample period. We find that in the exchange rate return series for South Korea, Taiwan and the Philippines, the random walk hypothesis is rejected at the 5% significance level in the M1 test.5 This would seem to indicate that the foreign exchange market of Japan is efficient; however, since the results using the M1 measure are obtained under an assumption of homoskedasticity, the rejection of the random walk hypothesis could well be due to heteroskedasticity. The results of the M2 test suggest that the rejection of the null hypothesis is not robust to heteroskedasticity for both Taiwan and South Korea, and the random walk behavior of Japan, South Korea and Taiwan cannot be rejected at any probability level under the M2 test. The rejection of efficiency in the foreign exchange market is also less significant for the Philippines (from 1 to 10%), which suggests that the difference in the variance ratio from the expected value could again be due to heteroskedasticity. We may infer from this that, with the exception of the Philippines, at k = 10 the foreign exchange markets of the countries examined are efficient. The non-parametric R1 and R2 test results for Japan, South Korea and the Philippines show that the random walk hypothesis cannot be rejected; that is, the foreign exchange markets of Japan, South

5

The rejection is much stronger for the Philippines than for Taiwan or South Korea.

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Table 3 Variance ratio tests, variance ratio tests with ranks and signs, and multiple-variance ratio testsa . Variance ratio tests for LTWDb

Variance ratio tests for LJPYb

kc

M1

M2

R1

R2

S1

kc

M1

M2

R1

R2

S1

2 5 10 15 20

0.56 1.12 1.42 1.99** 2.45***

0.31 0.63 0.84 1.23 1.57

−0.63 0.29 1.13 1.71* 2.25**

−0.48 0.53 1.46 2.09** 2.64***

2.70*** 4.75*** 7.11*** 8.80*** 10.14***

2 5 10 15 20

0.98 0.32 0.26 0.2 −0.04

0.6 0.22 0.19 0.15 −0.03

−0.86 −1.63 −1.16 −0.62 −0.65

−0.45 −1.16 −0.85 −0.54 −0.63

−1.22 −1.58 −0.76 −0.18 −0.28

SMMd

2.45*

1.57

2.25*

2.64**

10.14***

SMMd

1.68

1.16

1.58

Variance ratio tests for LPHPb

0.98

0.6

Variance ratio tests for LKRWb

k

M1

M2

R1

R2

S1

kc

M1

M2

R1

R2

S1

2 5 10 15 20

0.67 −2.72*** −4.45*** −3.29*** −2.72***

0.25 −1.07 −1.90* −1.49 −1.29

−1.35 −1.29 0.06 0.91 1.57

−0.61 −0.9 −0.24 0.61 1.24

−1.73* −1.21 0.52 1.29 1.99**

2 5 10 15 20

−0.25 −2.06** −3.34*** −2.47*** −2.22**

−0.08 −0.71 −1.16 −0.85 −0.77

−0.13 −0.32 0.21 0.68 0.98

0.55 −0.18 0.02 0.41 0.61

0.04 0.16 1.19 1.76** 2.30**

1.57

1.24

3.34***

1.16

0.98

0.61

c

SMMd

4.45***

1.9

1.99

SMMd

2.3

a

*** indicates significance at the 1% level; ** indicates significance at the 5% level; and * indicates significance at the 10% level. b LJPY refers to the Japanese Yen, LKRW refers to the South Korean Won, LTWD refers to the Taiwan Dollar, and LPHP refers to the Philippines Peso; all are in relation to the US dollar. c The term, k, refers to sampling intervals, in days. d The respective 1%, 5% and 10% significance levels of SMM are 3.0890, 2.5687 and 2.3106.

Korea and the Philippines are found to be efficient. Conversely, the random walk hypothesis is rejected for Taiwan at k = 15 and k = 20, irrespective of whether this is assessed under the R1 or R2 test. As regards the variance ratios on signs (S1 ), we find that for Japan, at all lags, the estimated results are not significantly different from 1, suggesting that the foreign exchange market of Japan is efficient. The related results for Japan conflict with those of Liu and He (1991) and Wright (2000); we surmise that a possible reason for this is the difference in the sample periods between those studies and the present one. Extremely diverse economic conditions, including changing government policies, can arise in different sample periods, factors which can clearly lead to very different assessments of efficiency within the foreign exchange market. Our sample period also covers the near future which can more adequately describe the state of the foreign exchange market in reality. Since the above empirical results are inconclusive with regard to South Korea, Taiwan and the Philippines, we further apply the SMM test of Chow and Denning (1993) to assist in determining which of the four markets, if any, exhibit consistent efficiency. The results of the SMM test show that the foreign exchange markets of Japan, South Korea and the Philippines are efficient for M2 , R1 , R2 , S1 . For Taiwan, even under consideration of multiple periods, the market remains inefficient. We infer that this may be due to intervention in the foreign exchange market by the government, or the impacts on the market from other related events. 2.3.2. Ratio of inefficiency through a rolling window Fig. 1a–d illustrates the test statistics for the rolling window application of the Wright (2000) test for R2 , for lags k = 2 and k = 5; the tests are run with 5% critical values.6 We find that as time goes by, the ratio of the variance will fall outside the 5% critical value, a phenomenon which indicates that during certain periods, the foreign exchange markets may be inefficient. Based on the above results, we go on to compute the ratio of variance for each floating exchange rate series so as to acquire both the extent and the ratio of inefficiency during the whole sample period. 6 For the purpose of saving space, in this paper we display only the graphs for Wright (2000) R2 , and for lags k = 2 and k = 5 tested with 5% critical values. Other graphs for M1 , M2 , R1 and S1 , and for lags k = 10, 15 and 20, are available on request.

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Fig. 1. (a) Wright’s rank-based R2 test results (lags 2 and 5) for Japan. Note: The horizontal line is the 5% critical value. (b) Wright’s ranks-based R2 test results (lags 2 and 5) for Korea. Note: The horizontal line is the 5% critical value. (c) Wright’s ranks-based R2 test results (lags 2 and 5) for Taiwan. Note: The horizontal line is the 5% critical value. (d) Wright’s ranks-based R2 test results (lags 2 and 5) for Philippines. Note: The horizontal line is the 5% critical value.

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Table 4 The inefficiency ratios of the selected countriesa . Variance ratio tests for LTWDb

Variance ratio tests for LJPYb

kc

M1

M2

R1

R2

S1

kc

M1

M2

R1

R2

S1

2 5 10 15 20

0.3345 0.312 0.1203 0.076 0.083

– – – – –

0.339 0.3115 0.2821 0.1151 0.074

0.3495 0.3221 0.2586 0.0895 0.0485

0.3025 0.5082 0.5562 0.5713 0.5408

2 5 10 15 20

0.193 0.0444 – – –

– – – – –

0.0803 0.0863 0.002 – –

0.0534 0.0349 0.001 – –

0.1421 0.0658 0.0075 – –

Variance ratio tests for LPHPb

Variance ratio tests for LKRWb

kc

M1

M2

R1

R2

S1

kc

M1

M2

R1

R2

S1

2 5 10 15 20

0.19 0.1282 0.1377 0.0225 0.009

– – – – –

0.0489 0.1392 0.1007 0.022 0.0405

0.0683 0.1451 0.0973 0.016 0.0145

0.009 0.0279 0.0873 0.1101 0.1096

2 5 10 15 20

0.0723 0.0748 0.0175 0.005 0.006

– – – – –

0.0529 0.0219 0.0115 – 0.003

0.0618 0.0379 0.0399 0.001 0.002

0.012 0.013 0.011 0.028 0.079

a

Wright (2000) is applied to compute the inefficiency ratio using a rolling window of size T = 250 observations. LJPY refers to the Japanese Yen, LKRW refers to the South Korean Won, LTWD refers to the Taiwan Dollar, and LPHP refers to the Philippines Peso; all are in relation to the US dollar. c The term, k, refers to sampling intervals, in days. b

By adding in all the available information, we can investigate and compare which markets of the four countries examined are more efficient. The related results are presented in Table 4. Table 4 shows that, in numerical terms, inefficiency is zero for the four foreign exchange markets when the computation is based upon the Lo and MacKinlay variance ratio test for M2 . This indicates that the exchange rate series of these markets seem to follow a random walk pattern. The efficiency sequence for the various sampling intervals, from the highest to the lowest, runs in the order of Japan, South Korea, the Philippines and Taiwan; i.e., the foreign exchange market of Taiwan is the least efficient. These results correspond with those presented in Table 2, revealing that the market of Taiwan does not follow a random walk pattern. The reason may be that in order to maintain economic development and the stability of the financial market in Taiwan, the government and the central bank may be restricting foreign exchange flows and frequently intervening in the foreign exchange market. Therefore, although Taiwan does have a so-called free-floating rate, its foreign exchange market is relatively inefficient. 3. Conclusions This paper re-examines the validity of the weak form efficient market hypothesis for the foreign exchange markets in four floating-rate Asian economies (Japan, South Korea, Taiwan and the Philippines). By using the Lo and MacKinlay (1988, 1989) traditional variance ratio test, the Wright (2000) non-parametric-based variance ratio test and the Chow and Denning (1993) multiple-variance ratio test, our investigation includes a considerable amount of information on the exchange rate series. We also adopt a fixed-sized rolling window of 250 observations to compute the extent of inefficiency, in numerical terms, and analyze whether such efficiency is consistent in the four countries examined. The three testing methods, the traditional variance ratio test, the variance ratio test based upon ranks and signs and the multiple-variance ratio test all produce the same inference, that the foreign exchange markets of Japan, South Korea and the Philippines are weak form efficient, while that of Taiwan is inefficient. We infer from this that the government and the central bank of Taiwan regard it as important to intervene in the foreign exchange markets. Therefore, although Taiwan does have a so-called free-floating rate, the foreign exchange market is relatively inefficient. Conversely, the foreign exchange markets of Japan, South Korea and the Philippines are all efficient.

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This study found the foreign exchange market is relatively inefficient in Taiwan. It is, however, possible to profit by observing the policies of the government and the central bank in Taiwan. These findings have practical implications, in terms of operations and forecasting for policymakers in general, and in particular, for both individual and institutional investors, each of whom can assess the risk and establish an optimum investment strategy to obtain excess returns. Therefore, we suggest that these policies show that the governments and central banks of yen-based block or some other Asian or Australasian exchange rate system are more compliant with foreign market functions; thus it is more difficult to predict the behavior of the exchange rates of yen-based block or some other Asian or Australasian exchange rate system. Appendix A. The variance ratio test of Lo and MacKinlay (1988, 1989) assesses the proportionality of the variance of k-differences from the first difference of the series. Lo and MacKinlay calculated that for a random walk series, the variance of its k-differences is k times the variance of its first difference. The variance ratio of the kth difference is defined as follows: VR(k) =

 2 (k)  2 (1)

(A1)

where VR(k) is the variance ratio of the kth difference of the series;  2 (k) is the unbiased estimator of 1/k of the variance of the kth difference of the series under the null hypothesis;  2 (1) is the variance of the first difference of the series; and k is the number of days in the observation interval, or difference interval. According to Lo and MacKinlay (1988, 1989), the estimator of the k-period difference,  2 (k), can be computed as follows: 1 2 (zt + ... + zt−k−1 − k) ˆ Tk T

 2 (k) =

(A2)

t=k

T

where  ˆ = (1/T ) culated as follows:

z. t=1 t

The unbiased estimator of the variance of the first difference,  2 (1), is cal-

1 2 (zt − ) ˆ T T

 2 (1) =

(A3)

t=1

The test statistic M1 (k) is therefore defined as follows: M1 (k) =

VR(k) − 1

(A4)

1/2

(k)

Under the assumption of homoskedasticity, M1 (k) is asymptotically distributed to N (0, 1), with the asymptotic variance,  (k), being defined as follows: (k) =

2(2k − 1)(k − 1) 3kT

(A5)

The test statistic M2 (k) is robust under heteroskedasticity and defined as follows: M2 (k) =

VR(k) − 1 ∗ (k)

where ∗ (k) =

(A6)

1/2

k−1  i=1

2

T

[(2(k − i))/k] ı(i), and ı(i) = (

t=i+1

2

2

T

(Zt − ) ˆ (zt−i − ) ˆ )/[

t=1

2 2

(Zt − ) ˆ ] .

Wright (2000) proposed the use of signs and ranks to substitute for the differences in the Lo and MacKinlay tests, demonstrating that for some processes, the non-parametric variance ratio tests based on ranks (R1 and R2 ) and signs (S1 ) can reject the violations of the random walk hypothesis far better

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293

than the tests proposed by Lo and MacKinlay. The R1 and R2 proposed by Wright (2000) are defined as follows:

⎛

⎞

T 

2

⎟ ⎜ (1/Tk) (r1t + ... + r1t−k+1 ) ⎟ ⎜ t=k ⎟ × (k)−1/2 R1 = ⎜ − 1 ⎟ ⎜ T  ⎠ ⎝ 2 r1t

(1/T )

(1/Tk)

R2 =

t=1

T

(r + ... + r2t−k+1 )2 t=k 2t

(1/T )

(A7)

T

r2 t=1 2t

 −1

−1/2

× (k)

(A8)



where r1t = (r(zt ) − ((T + 1)/2))/ (T − 1)(T + 1)/12 r2t = ˚−1 r(zt )/(T + 1). (k) is as defined in Eq. (A8); r(zt ) is the rank of zt among zt , . . ., zT ; and −1 is the inverse of the standard normal cumulative distribution function. The test based on the signs of the returns is defined as follows7 :



S1 =

(1/Tk)

T t=k 1 T

(st + ... + st−k+1 )2

T

s2 t=1 t



−1

−1/2

× (k)

(A9)

0.5 if z, > q ; S therefore assumes a zero drift value. −0.5 otherwise 1 In this study we use the multiple-variance ratio test proposed by Chow and Denning (1993) to ascertain the degree of autocorrelation and heteroskedasticity in the returns. Based upon the Lo and MacKinlay (1988) single variance ratio test, Chow and Denning (1993) computed the variance ratio covering all possible intervals. They therefore demonstrated that the multiple-variance ratios can generate a procedure for compound comparisons of the set of variance ratio estimates with unity. Consider a set of m variance ratio tests, {h(kj )|j = 1, 2, . . ., m}, in which there are multiple subhypothesis under the random walk null hypothesis; that is where st = 2 (zt , 0), u(zt , q) =

H0 j : h(kj ) = 0 for j = 1, · · ·, m and H0j : h(kj ) = / for any j = 1, · · ·, m If one or more H0j is rejected, then the random walk hypothesis is also rejected. Since the random walk null hypothesis will be rejected if any of the estimated variance ratios is significantly different from 1, it is therefore necessary to focus only on the maximum absolute value in the set of test statistics. The Chow and Denning (1993) multiple-variance ratio test is based on the results: PR[max(|h(k1 )|, · · ·, |h(km )| ≤ SMM(˛; m; T )] ≥ 1 − ˛

(A10)

where h(kq ) = {M1 (kq ), M2 (kq ), R1 (kq ), R2 (kq ), S1 (kq )}, SMM (˛; ∞; T) is t/he upper ˛ point of the ‘standardized maximum modulus’ (SMM) distribution with m parameters (number of variance ratios) and T (sample size) degrees of freedom. Asymptotically, when T is infinite: SMM(˛; m; ∞) = Z(1−(1−˛)1/m )/2

(A11)

where Z(1−(1−˛)1/m )/2 follows a standard normal distribution. The size of the multiple-variance ratio test is controlled by comparing the calculated values of the standardized test statistics using the SMM critical values proposed by Miller (1981); for large samples, these can also be generated from the standard normal distribution using Eq. (A11). If the maximum absolute value of h(kq ) is greater than the SMM critical value at a predetermined significance level, then the random walk hypothesis is rejected.

7 Wright (2000) noted that the sign-based variance ratio test statistic, S2 , was conservative in finite samples and was expected to have relatively low power because the probability of rejection under the null hypothesis is always less than, or equal to, the nominal level in all sample sizes. For this reason, this test statistic is abandoned in this paper.

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