The European exchange rates before and after the establishment of the European Monetary System

Journal

Journal of International Financial Markets, Institutions and Money 7 (1997) 235-253

ELSEVIER

"f

INTERNATIONAL FINANCIAL MARKJZTS, INSTITUTIONS & MONEY

The European exchange rates before and after the establishment of the European Monetary System Michael Y. Hu *, Christine X. Jiang, Christos Tsoukalas Graduate School o$Management,

College of Business Administration. OH 44242-0001, USA

Kent State University, Kent.

Abstract The present study examines the performance of a number of alternative GARCH/EGARCH models in the pre- and post-EMS periods. Our empirical results render support for EGARCH specifications in modeling bilateral exchange rates. The fact that EGARCH models are able to characterize the behavior of EMS rates is consistent with the unique features of the EMS as a managed-float regime. The existence of a band for EMS rates calls for interventions from the central banks whenever a particular pair of rate moves outside the band as a result of a large shock, or successive shocks in the same direction. The EGARCH models, with its ability in modeling the magnitude as well as the directions of shocks, are particularly relevant for capturing the temporal relationships between shocks in currency movement and future conditional volatility. In addition, we also find that the EMS arrangements are quite effective in reducing the conditional and unconditional volatility in the currency market. 0 1997 Elsevier Science B.V. Ke~ords; JEL

Conditional

clas$cation:

volatility;

EGARCH

model; EMS exchange

rates

C32; F31

1. Introduction The European Monetary System (EMS) was founded in December 1978 with the intention to replace the earlier ‘Snake’ system which had failed to stabilize the European currencies. The EMS, with its operations started in March 1979, aimed to increase the economic convergence of the member economies through reducing the volatility of their currencies. Through a set of monitoring mechanisms based on economic variables such as interest rates and inflation, the EMS authorities track the convergence of the member economies and enforce the currency target zone.’ * Corresponding author. ’The EMS, however, does not impose restrictions on its member currencies relative to other major currencies such as the dollar and the yen. 1042~4431/97/$17.000 1997 Elsevier Science B.V. All rights reserved PII SlO42-4431(97)00021-8

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M. Y Hu et al. / ht. Fin. Markets. Inst. and Money 7 (1997) 235-253

The zone was initially set at f2.25% (f6% for the Italian lira) around the central parity rates,’ but after the foreign exchange market crisis of August 1993 the zone became + 15%. The band is enforced with the help of a divergence indicator which alerts the monetary authorities of the member states whenever a bilateral exchange rate moves too close to the floor or ceiling of the zone (Lieberman, 1992). If the divergence exceeds f75% of the maximum divergence allowed, intervention is carried out by the two central banks involved. Fundamental disequilibriums are usually fixed through realignments. Twenty realignments have occurred thus far, most of them in the early years of the system and a few after 1990. Previous studies on EMS rates have placed emphasis on the following two areas. Many researchers have examined the impact of the establishment of the EMS on a number of economic variables ranging from inflation and interest rates to exchange rate volatility (Artis, 1990). Regarding exchange rates, most previous research has focused on what Williamson (1983, 1985) calls “high-frequency instability”, that is, exchange rate volatility over short periods of time. The evidence on high-frequency conditional instability within the EMS is rather limited. Diebold and Pauly (1988) examined the impact of the establishment of the EMS on the exchange rates of the French franc and Italian lira versus the German mark. Through a bivariate ARCH model, they detected a structural shift at the time of the inception of the EMS and a drop in conditional volatility of both currencies after March 1979. The observations derived from a relatively small sample of currencies, however, are difficult to generalize. Bollerslev (1990) conducted a more extensive study. He used a multivariate GARCH( 1, 1) model to examine the conditional characteristics of the German mark, French franc, Italian lira, Swiss franc and British pound before and after the creation of the EMS. He detected a decrease in conditional volatility and greater coherence among the European exchange rates after the creation of the EMS. His findings are subject to certain limitations. First, all exchange rates are measured versus the US dollar, which is highly volatile, especially in the 1980s. The fact that the EMS only places restrictions on volatility of bilateral exchange rates within its own system with no efforts made on reducing dollar related volatility, may inject noise into the data and make statistical tests less powerful. Second, the distributions of the exchange rates may not be identical for each member currency, and using a multivariate GARCH model to fit all the exchange rates may not be appropriate. More recently, Nieuwland et al. (1994) examined the conditional nature of the EMS exchange rates in a univariate AR( 1)-jump-GARCH( 1, 1) framework. Their dataset included the exchange rates of all EMS currencies (as of 1992) against the German mark. Their model explained the log returns quite well, but did not attempt to explain whether differences exist for distributions of exchange returns during pre-EMS versus the EMS period. The other strand of research has focused on the behavior of the EMS rates. Routmos (1994) found significant first-order autocorrelations in the means when the autocorrelations are modeled as a function of conditional volatility. Motivated 2 Within the EMS, other currencies were relatively less important, so that the central exchange rate is dominated by the exchange rate between the franc and mark.

M. Y. Hu et al. ; ht. Fin. Markets, Inst. and Money 7 ( 1997) 235-253

137

by a growing number of studies reporting asymmetry behavior between shocks and future volatility in the stock market, exponential GARCH models (EGARCH ) are also applied to exchange rates. Empirical evidence on asymmetry was provided by Kahya et al. (1994) and Koutmos (1994). In their paper, the asymmetry in the conditional volatility was documented for several EMS and non-EMS currencies. However, due to the two-sided nature of currency (Bollerslev et al., 1992), the authors found it harder to explain why depreciation and appreciation should be perceived differently by market participants. A limitation in their studies is related to the fact that they used bilateral exchange rates measured against the US dollar. Since EMS is an arrangement among member currencies, there is no direct implication on how the EMS should affect the behavior of bilateral rates between the dollar and European currencies. Thus a finding of asymmetry can not be directly attributed to the EMS. The objective of this paper is to provide further empirical evidence on the EMS exchange rates. Recognizing that the ‘leverage effect’ which is the motivation for many applications of EGARCH models on stock prices may not be relevant in the currency market, we suggest that asymmetry between volatility and shocks may exist due to the EMS arrangement, that is the existence of bands among bilateral rates. To capture the impact of the distinctive feature of the EMS band on the time path of exchange rate movement,3 the appropriate data sample should be all EMS rates measured against the Deutsche mark. Within an EMS framework, intervention is expected to depend highly on the deviations from central rates and indirectly on the volatility. Interventions may not be required if the shocks change directions frequently and are never large enough to move exchange rates outside the band. Therefore, both the sign and the magnitude of deviation play a significant role in modeling the EMS rates. The EMS setting makes it particularly meaningful to separate the effect of positive and negative shocks (appreciation versus depreciation) and to examine the persistency of those shocks. Conventional GARCH models fail to recognize the different implications of shocks of different directions (Nelson, 1991). EGARCH4 modifies the Bollerslev ( 1987) conventional GARCH in providing a model specification which allows separate effects of ‘good’ and ‘bad’ news, and also a structure to examine the persistence of the volatility. Although it is difficult to judge whether a shock in the currency market (e.g. an unexpected depreciation) is ‘good’ or ‘bad’ news in general, we believe that we are in much a better position to evaluate the effect of a surprise in the currency market for EMS rates, since currency stability is one of the main objectives of the EMS. Most of the previous studies have used prior knowledge to select a single GARCH model to examine the conditional volatility of the EMS exchange rates. The present paper goes a step further by using a wide range of GARCH models to explain the

3 In some sense, the EMS structure resembles the features of a stationary process with symmetric. reflecting barriers. ’ The EGARCH model is particularly useful in explaining the ‘leverage etfect’ which suggests that bad news on security returns results in a higher leverage, and the market tends to perceive the equity being riskier than before the shock (Black. 1976).

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M. Y. Hu et al. / ht. Fin. Markets, Inst. and Money 7 (1997) 235-253

log returns of all the bilateral (against the German mark) EMS exchange rates. Instead of imposing a certain structure for the conditional first and second moments, we make use of the information contained in the data series to help us gauge the appropriate model structure for each bilateral exchange rate. Univariate rather than bivariate or multivariate GARCH models are selected in order to account for the potentially different characteristics of each EMS rate. The nature of the study allows us to provide evidence on a number of issues. First of all, is the conventional GARCH model or the EGARCH specification more consistent with the EMS rates? Does the model specification change before or after the establishment of the EMS? Second, does asymmetry exist in the EMS rates? In particular, what is the nature of the relationship between surprises in currency return and conditional volatility? Third, has the conditional, unconditional volatility decreased after the establishment of the EMS? The rest of the paper is organized as follows. Section 2 describes the dataset of exchange rates. Section 3 presents the results of the analysis starting with some diagnostic statistics and continues with the estimates of the alternative models. The paper ends with a summary of the findings and conclusions in Section 4.

2. Research methodology 2.1. Dataset The dataset includes weekly (Wednesday) spot exchange rates of the period from 8 January, 1975 to 30 October, 1991. The data were obtained from Datastream. Wednesday rates were chosen to avoid holidays (Diebold and Nerlove, 1989) and weekend effects (Hsieh, 1989; Lastrapes, 1989). The currencies examined in the study are those of the first 12 members of the European Union (EU), namely, the British pound, the Belgian/Luxembourg franc, the Danish kroner, the French franc, the German mark, the Greek drachma, the Irish punt, the Italian lira, the Dutch guilder, the Portuguese escudo, and the Spanish peseta. Since both Luxembourg and Belgium use the Belgian franc and all rates are against the German mark, the dataset consists of 10 exchange rates ‘. The sample period starts roughly 1 year after the unofficial collapse of the ‘Snake’ system and ends 1 year before the spasm that seized the foreign exchange markets in September 1992 and forced the British pound and the Italian lira to exit the system. The whole study period is split into two subperiods: from 1 January, 1975 to 7 March, 1979 (pre-EMS subperiod), and from 14 March, 1979 to 30 October,

5 Although not all of the EU member currencies participated in the EMS during the whole study period, the assumption in this study is that they can be thought of as EMS currencies. The reason is that every EU member country has the obligation to eventually join the EMS and in order to do so its currency should conform to EMS-like properties (stability for example) well in advance.

hf. Y. Hu et al.

,’ht. Fin. Markets, Inst. and Monq, 7 ( 1997) 235-253

239

199 1 (the EMS subperiod). The event used for dividing the data into two subperiods is the establishment of the EMS on 13 March. 1979. fian~e~cwk

2.2. The GARCH

Financial series such as stock prices and exchange rates have long exhibited clustering of volatility along with leptokurtic unconditional variances. To address these issues, the ARCH model (Engle, 1982) was proposed to model the temporal variations in the volatility process. The approach is based on the presumption that forecasts of variance at some future point in time can be improved by using prior information. The conditional mean models of the 1970s (i.e. ARMA) were based on the same presumption about the mean. The conditional volatility models have been shown to be quite effective in modeling financial time series which tend to cluster together. The other appealing feature of the model lies in its ability to distinguish conditional (predictable) and unconditional (total ) volatility (Artis, 1990). The time varying volatility models are expected to shed some light on the conditional volatility of an asset price which is predictable and, therefore, less costly to hedge. In particular, the use of ARCH models with exchange rate data leads to conditional normal distributions and symmetric but leptokurtic unconditional ones that closely resemble the empirical distribution of exchange rates (Burt et al., 1977: Friedman and Vandersteel, 1982). Bollerslev ( 1986) extended the ARCH model to account for a more flexible lag structure in the variance equation. In addition to historical shocks, lagged conditional volatility are also included in the conditional variance equation. The lag structure is usually assumed to decline over time to be consistent with the conjecture that recent shocks tend to affect the series more strongly. In order to ensure that conditional volatility is meaningful, nonnegativity constraints are also imposed on the parameters of the variance equation. The GARCH structure allows for a drawnout effect on the conditional variance or ‘longer memory’. Whenever the sum of the ARCH (ri) and GARCH (Bj) coefficients is equal to 1, integration-in-variance is present which means that “. ..current information remains important for the forecast of the conditional variances for all horizons” (Engle and Bollerslev, 1986). In this case, the conditional variance n steps in the future depends on the same information as the conditional variance one step ahead, for any horizon n. The first group of specifications tested is the GARCH (p. q) models: e,I(@,,_,-D(O,h,),

yt=Co+e,, ht = Wo + i

aief-i + f_ pjh,_j,

i=l

j=l

where

St

( 1

y, = 100x In -

St-*

’

(1)

240

M. Y. Hu et al. J ht. Fin. Markets, Inst. and Money 7 (1997) 235-253

and S, is the spot exchange rate on Wednesday (e.g. FF/DM, UKL/DM, HFL/DM, etc.). C is an unknown parameter; D(O,h,) denotes a distribution with zero mean and time-varying variance h,. Given the fact that prior studies on asset prices (Bollerslev et al., 1992) suggest that lower-order GARCH models tend to be parsimonious yet effective in capturing the time variation in residuals, we examine in this study two specifications within the GARCH family, namely, GARCH( 1, 1) and GARCH(2, 2). Given the nature of the EMS arrangements, the second group of model used is the exponential GARCH (EGARCH) model suggested by Nelson (1991). In contrast to the conventional GARCH specifications which require nonnegative coefficients, EGARCH models do not impose the nonnegativity constraints on the parameter space (Nelson and Cao, 1992). The simple GARCH(p, 4) model can capture thick-tailed returns and volatility clustering, but fails to distinguish potentially different impact of shocks of different directions. The reason is that the conditional variance is simply a function of the magnitudes of the lagged residuals and not of their signs in GARCH models. The EGARCH model can account for the direction of shocks because it has the same mean equation as the simple GARCH(p, q) model, but the conditional variance (h,) is an asymmetric function of the lagged residuals: ln(h,)= Wo + i

xig(Z*-i)+ i

i=l

j=l

flj

ln(h,-j),

(3)

where

g(z,)= & + Iz,I-4ztL and

In this study, we consider two specific models, namely EGARCH( 1, 1) and EGARCH(4, 4). One last modification to the specifications discussed above is to include an autoregressive process in the mean equation to account for the possible autocorrelations together with GARCH/EGARCH errors. The AR(k)-GARCH(p, q) and AR(k)-EGARCH(p, q) models have the same variance equation as the GARCH(p, q) or the EGARCH(p, q) models, but the following mean equation: (4) Three additional models, AR( 1)-GARCH( 1, 1), AR( 5)-GARCH( 1, 1) and AR(S))EGARCH(4, 4) will be examined. A variety of specifications that allow differences in mean equation (a random walk versus an autoregressive process) and in variance equation (GARCH versus EGARCH) will be examined. Model comparisons within each group of specification

Dutch guilder Belg./Lux. franc

Italian lira

1975 to 30 October,

6.1816 66.8373 126695** 0.0057 (0.0389) -0.0241 (0.0389) 24.86 2.31

-0.6392 3.9967 134.77** -0.2087 (0.0677) 0.1163 (0.0706) 52.83** 38.13

0.0172 0.3660 - 1.9096 16.7326 2359.87** - 0.4045 (0.0677) 0.1482 (0.0780) 80.15** 42.67

0.0258 0.4776

0.3337 2.1453 147.21** 0.1134 (0.0389) 0.0137 (0.0394) 46.40* 87.94**

0.1631 18.4937 9085.73** -0.2666 (0.0389) -0.0039 (0.0416) 64.78** 136.3 1**

4.8755 69.2522 132785** -0.1867 (0.0389) -0.0085 (0.0403) 68.83** 10.45

1979 to 30 October, 1991 (NOBS=660) 0.0066 0.0410 0.0394 0.263 1 0.5037 1.1205

0.9561 4.5303 274.60** 0.1355 (0.0677) -0.0011 (0.0690) 33.75 32.03

1.2645 6.3299 486.91** 0.0760 (0.0681) 0.2025 (0.0681) 36.20 19.62

14 March, 0.0595 0.4709

0.1864 1.1132

0.1040 0.7546

2.4877 16.7421 8970.81** -0.1334 (0.0389) -0.0031 (0.0396) 55.29** 33.52

0.0763 0.5277

0.8862 22.4840 4106.43** -0.00841 (0.0677) 0.0285 (0.0677) 44.89* 81.55**

0.2401 1.3406

(LIT) (J-JFL) (B/LFB) (UKL) Versus German mark (DM) Pre-EMS subperiod: 8 January, 1975 to 7 March, 1979 (NOBS=218)

British pound

*Statistically significant at the 5% level, **Statistically significant at the 1% level.

LB (30) LB2 (30)

P(2)

P(l)

EMS-subperiod: Mean Standard deviation Skewness Kurtosis BJ Test

LB (30) LB2 (30)

P(2)

P(l)

Mean Standard deviation Skewness Kurtosis BJ Test

Statistic

French franc ( FF f

1 Summarystatisticsof the weekly log returns. Period: 8 January,

Table

1.9107 16.2580 7942.08** -0.1274 (0.0389) -0.0253 (0.0396) 54.24** 21.07

0.0495 0.4323

0.6454 3.8788 179.13** -0.0665 (0.0677) 0.0148 (0.0699) 47.76* 46.31*

0.0832 0.6108

Danish kroner (DKR)

4.3460 52.0853 76194** -0.0918 (0.0389) 0.0223 (0.0393) 49.38* 5.75

0.0530 0.4778

0.9561 4.5303 274.60** 0.1355 (0.0677) -0.0011 (0.0690) 33.75 32.03

0.1864 1.1132

Irish punt (IRL)

1991 (878 weekly observations)

6.6363 82.3530 176993** -0.0532 (0.0389) 0.0363 (0.0390) 26.60 1.18

0.2640 1.2202

- 3.8430 34.4585 9132.35** 0.1795 (0.0677) 0.0134 (0.0699) 35.50 8.65

0.1308 1.1585

Greek drachma (DBA)

1.0530 3.6913 39.6150 43784** -0.0850 (0.0389) -0.0008 (0.0392) 53.65** 8.68 3.3010 39.9944 44990’ * 0.0395 (0.0389) 0.1120 (0.0390) 38.23 1.51

0.1833

8.8671 104.8234 81206** 0.0225 (0.0677) 0.0334 (0.0678) 8.24 0.42

0.4253 1.3292

(ESC)

Portuguese escudo

0.0797 0.7890

9.2194 105.8844 102110** 0.0464 (0.0677) -0.0125 (0.0679) 7.00 0.44

0.2170 1.9047

(PTA)

Spanish peseta

-80.61 42.52** 49.00s** - 77.79 31.37** 47.s9* 5.64 -78.15 53.a9** SO.23* 4.92** -0.72 - 77.32 55.30** 50.29* 6.58 0.94 1.66 (3)

- 326.96 292.58** 26.76 1.74

- 326.43 336.95** 27.99 2.80 1.06

-323.03 288.99** 28.51 9.60 7.86 6.80

(1)

(HFL)

(URL)

(FF)

subperiod:

(3)

-99.22 967.72** 35.46 15.94* 15.84* 6.14

- 102.29 818.90** 36.96 9.7* 9.7*

- 107.14 770.42** 33.38 0.00

- 107.14 765.40** 33.41

( B/LFR)

Belg/Lux franc

Pre-EMS

- 327.83 310.66** 27.91

Dutch guilder

British pound

French franc

models to the log returns.

GARCH models Model 1: GARCH(1, 1) - 235.39 Log-L 167.61** BJ test 34.95 LB (30) Mode1 2: GARCH(2, 2) -234.67 Log-L 153.04** BJ test 35.95 LB(30) 1.44 LR test: (I) and (2) Model 3: AR(l)-GARCH(1, 1) -234.99 Log-L 186.161** BJ test 34.96 LB(30) 1.00 LR test: (1) and (3) -0.44 LR test: (2) and (3) Model 4: AR(S)-GARCH(l, 1) -230.78 Log-L l27.57** BJ test 34.46 LB( 30) 9.22 LR test: (I) and (4) 7.78 LR test: (2) and (4) 8.22 LR test: (3) and (4) Best GARCH model (1)

Estimate

Table 2 Results from fitting alternative

(4)

-307.11 393.28** 24.45 11.62 14.66* 11.54

-312.88 674.50** 28.81 0.08 3.12

-314.44 869.77** 22.54 -3.04

-312.92 697.67** 28.97

(LIT)

Italian lira

8 January,

(1)

- 193.35 208.7** 40.09 0.72 0.72 0.18

- 193.44 206.99** 40.21 0.54 0.54

- 193.71 189.16** 40.53 0.00

- 193.71 189.16** 40.53

(DRR)

Danish kroner

(1)

-323.03 0 288.99** 29.51 9.60 7.86 6.80

- 326.43 336.95** 27.99 2.80 1.06

- 326.96 282.58** 26.76 1.74

(3)

-319.39 2132.23** 38.74 12.16 12.16* 3.90

-321.34 2513.77** 37.90 8.26* 8.26*

-325.47 4367.73** 38.66 0.00

- 325.47 4367.7** 38.66

(DRA)

Greek drachma

(1)

-448.57 102417** 7.00 1.44 1.44 0.96

- 449.05 99385** 7.00 0.48 0.48

-449.29 100244** 7.00 0.00

- 449.29 100244** 7.00

(PTA)

Spanish peseta

1979 (218 weekly observations)

- 327.83 310&i** 27.91

(LRL)

Irish punt

1975 to 7 March,

(1)

-370.49 97751** 8.24 0.76 0.76 0.64

-370.81 97602** 8.24 0.12 0.12

- 370.87 98076** 8.24 0.00

- 370.87 98076** 8.24

(ESC)

Portuguese escudo

-

- 53.68 4.13 42.75 43.92* -47.51 3.15 49.60* 56.14* 12.22 (6)

- 304.70 8.66* 25.64 24.52*

-288.18 4.47 25.82 57.56* 33.04*

(7)

in bold.

-15.64 21.26** 43.15

- 3 16.96 210.61** 22.11

*Statistically significant at the 5% level. **Statistically significant at the 1% level. The best model within each group is highlighted

EGARCH models Model 5: EGARCH( 1, 1) Log-L - 226.14 BJ test 50.34** LB(30) 41.29 Model 6: EGARCH(4. 4) Log-L - 203.62 BJ test 5.84 LB(30) 49.02* LR test: (5) and (6) 46.24* Model 7: AR(S)-EGARCH(4,4) Log-L -212.14 BJ test 21.45** LB(30) 46.63* LR test: (5) and (7) 29.20* LR test: (6) and (7) - 17.04 Best EGARCH model (6) (7)

- 65.41 12.40** 61.79** 77.72* 41.64*

- 86.23 103.20** 38.27 36.08*

- 104.27 980.52** 32.65

(7)

- 272.92 19.54** 30.66 46.10* 21.44*

- 283.64 36.69** 26.95 24.66*

~ 295.97 260.05:; 31.15

(7)

- 162.02 5.60 44.58* 57.34* 29.54*

- 176.79 30.43** 46.10* 27.80*

- 190.69 129.75** 39.70

(7)

- 288.18 4.47 25.82 51.56* 33.04*

- 304.70 8.66* 25.64 24.52*

-316.96 210.61** 22.11

- 261.33 42.60** 19.19 86.30* 24.98*

- 257.73 3.66 43.59 116.32* 5.00

(7)

- 279.82 21.388** 22.47 61.32*

- 260.23 4.06 33.33 111.32*

(6)

- 310.48 964.33** 18.08

-315.89 1343.36** 31.77

s 87.95** 45.57*

(6)

-10.08 93.56*

i s ?

2

,” : ar-. . ..

37.56 103.64* -254.37

F .Y

249.33 124.13**

-301.15 16133** 24.62

-472.89 3492.33** 33.53 27.60* 25.48* -469.18 3342.44** 33.52 9.54 - 18.06 7.42 (2)

-351.36 8157.14** 67.77** 20.18* -40.14 - 348.49 8232.44** 67.62** 66.06* 45.88; 5.74 (3)

105.57 2943.27** 58.85** 38.36* - 12.08 108.57 3063.35** 60.74** 44.36* 18.08* 6.00 (3)

- 979.69 159.11** 44.69* 9.74 5.14 2.64

(1)

-981.01 167.92** 44.23* 7.10 -2.50

-460.15 3472.98** 38.13 27.60*

-371.43 9765.80** 61.45** 20.18:

99.53 1752.63** 44.37* 26.28*

-982.26 205.73** 42.74 4.60

(LIT)

(B/LFR)

(2)

- 354.40 4092.38** 41.78 13.78* 4.66 3.92

- 356.36 4213.45** 41.99 9.12* -0.74

- 356.73 4196.55** 44.39* 9.12*

-361.29 3751.28** 42.94

(DRR)

Danish kroner

1979 to 30 October,

-473.95 3094.94** 32.64

Italian lira

Belg/Lux franc

14 March,

-381.52 8970.84** 65.74**

(HFL)

86.39 3079.37** 44.40*

(‘JRL)

(FF)

Dutch guilder

EMS subperiod:

-984.56 191.14** 44.26*

British pound

French franc

models to the log returns.

GARCH models Model 1: GARCH(1, 1) -362.70 Log-L 105994** BJ test 26.42 LB(30) Model 2: GARCH(2, 2) - 349.08 Log-L 47660** BJ test 28.59 LB(30) 27.24* LR test: (1) and (2) Model 3: AR(I)-GARCH( 1, 1) -367.26 Log-L 46710** BJ test 21.30 LB(30) LR test: (1) and (3) -9.12 LR test: (2) and (3) 36.36* Model 4: AR(5)-GARCH(1, 1) -310.31 Log-L 24%8** BJ test 32.47 LB( 30) LR test: (1) and (4) 104.78* 77.54* LR test: (2) and (4) LR test: (3) and (4) 113.90* Best GARCH model (4)

Estimate

Table 3 Results from fitting alternative

(4)

-351.56 17&19** 51.77** 59.18* 53.90* 36.90*

- 370.01 30452** 48.91** 5.28; - 17.00

-378.51 32124** 40.61 5.2800

-381.15 35467** 47.61*

(IRL)

Irish punt

(4)

- 852.27 2755.39** 41.44 89.80* 83.86* 22.46*

- 863.50 4559.86** 41.70 5.94* -61.40

- 894.20 13172** 37.83 5.9400

-897.17 11970** 39.05

(DRA)

Greek drachma

(4)

-755.18 10712** 42.10 48.86* - 10.66 47.82*

- 779.09 44106** 38.23 59.52* 58.48*

-749.85 6411.10** 35.70 59.52*

-779.61 44499** 38.23

(PTA)

Spanish peseta

1991 (660 weekly observations)

(2)

-917.02 26152** 36.18 19.30* - 10.66 6.32

-920.18 28454;; 36.31 29.96* 16.98*

-911.69 15976** 42.70 29.96*

- 926.67 18911** 46.97*

(ESC)

Portuguese escudo

- 172.96 326.74** 47.95* - 43.9 - 168.32 693.13** 46.19 - 34.62 9.28 (5)

-979.02 95.24** 46.28* 15.5*

- 969.57 119.34** 43.61 34.40* l&90*

(7)

in bold.

- 151.01 881.80** 44.9**

- 986.77 244.14** 44.83*

*Statistically significant at the 5% level. **Statistically significant at the 1% level. The best model within each group is highlighted

EGARCH models Model 5: EGARCH( 1, 1) Log-L - 322.52 BJ test 67648** LB(30) 27.67 Model 6: EGARCH(4,4) Log-L -216.19 BJ test 8387.38** LB(30) 32.11 LR test: (5) and (6) 212.66* Model 7: AR(S)-EGARCH (4, 4) Log-L - 186.34 BJ test 1648.97”” LB( 30) 30.78 LR test: (5) and (7) 272.36* 59.70* LR test: (6) and (7) (7) Best EGARCH model (7)

- 242.82 1205.94** 64.55** 400.82’ 170.72*

-328.18 3416.78** 56.85** 230.01*

-443.23 180098** 64.27**

(6)

-422.37 1319.92** 47.44’ 48.2* - 59.68

- 392.53 773.79** 37.03 107.88*

-446.47 2423.85** 38.54

(7)

- 297.47 1347.92** 37.97 67.32* 20.04*

- 307.49 1498.69** 36.59 47.28:

-331.13 1956.36** 38.44

(7)

- 266.29 870.01** s&45** 211.26* 14.92*

- 273.75 1077.88** 60.98** 198.34*

- 371.92 19919** 46.78*

(7)

- 782.17 85.32** 38.49 227.98* 80.98*

- 822.66 176.76** 37.20 14.70*

-896.16 12048** 32.92

(6)

- 712.69 1131.04** 40.70 62.88* 7.14

-716.26 982.83** 41.11 55.74*

-744.13 4101.71** 35.47

(6)

-811.01 668.19** 52.23** 222.24* - 15.62

- 803.20 509.28** 47.40* 237.86*

-922.13 13127** 54.70**

246

hf. Y. Hu et al. /ht.

Fin. Markets. Inst. and Money 7 (1997) 235-253

are conducted by performing a likelihood ratio test. However, since GARCH and EGARCH specifications are not nested, a general form of specification which encompasses both the GARCH and EGARCH models (Engle and Ng, 1993) is required. For a comparison between the best model in the GARCH class and the best one in the EGARCH class, the following likelihood function is used: ln(h,)=ln

IV,+ i ( + f i=l

Uie,_i+ i

i=l

yr(e,-i/c)+

/?j lIl(h,_j)

+ f )

j=l

/IJ lIl(h,_j)

j=l

f @~(le~-iI/~-V%)

(5)

i=l

With this specification, it is clear that the GARCH(p, q) model is a special case when af = $ = r’ = 0; and the above full model has a reduced-form corresponding to an EGARCH(p*, q*) when ai =pj =O.

3. Results Table 1 presents some summary statistics on the weekly log returns of the 10 exchange rates for each subperiod. The mean changes for all rates are positive, indicating depreciation against the German mark. The return distributions of most rates are positively skewed and leptokurtic in both subperiods. The Bera and Jarque ( 1982) joint test of skewness and kurtosis (BJ Test) consistently rejects the normality hypothesis for all rates. The kurtosis coefficients for all but four rates (the British pound, the Italian lira, the Spanish peseta and the Portuguese escudo) increase from the pre-EMS to the EMS subperiod. Comparisons across subperiods reveal that all mean log returns (except for the Belgian/Luxembourg franc and Greek drachma) decrease after the creation of the EMS. The Portuguese escudo has the largest depreciation against the German mark in the pre-EMS subperiod and the Greek drachma in the EMS subperiod. The Dutch guilder has the smallest depreciation in both subperiods. The fact that the Dutch guilder is pegged to the German mark is reflected in the standard deviation of its returns, which is the smallest in both subperiods. Table 1 also presents some autocorrelation statistics on the log returns of the 10 exchange rates. The first-order serial autocorrelation coefficients with their standard errors are reported followed by the Ljung-Box statistics (Ljung and Box, 1978) for kth (k = 30) order serial correlation of the log returns [LB (30)] and their squares [LB2(30)]. Significant autocorrelation of the squared series is an indication of conditional heteroscedasticity (Bollerslev, 1987; Hsieh, 1989). Stronger autocorrelations are present after the establishment of the EMS. The fact that exchange rate movements have to move within a target zone is quite consistent with our findings of significant autocorrelations. The results on various univariate GARCH/EGARCH models are reported in Table 2 (pre-EMS subperiod) and in Table 3 (EMS subperiod). The estimation process uses the quasi-Newton iterative algorithm. Several statistics for each model

M. Y. Hu et ul. ! Int. Fin. Murkets.

Inst. und Mnne~~ 7 i 1997) 235-253

247

are displayed, including the maximum value of the log-likelihood function (log-L) and diagnostic statistics such as the Bera-Jarque statistic (Bera and Jarque, 1982) of normality of the standardized residuals e,/(/~,)“~, and the Ljung-Box (Ljung and Box, 1978) statistic of white noise of the 30th order for the standardized residuals. In order to compare the model performance on an equal footing, generalized likelihood ratio tests are performed on pairs of nested models. The best model within each group is reported. As we noted earlier, one complication lies in that GARCH and EGARCH specifications are not nested, and thus comparisons based on likelihood ratios are no longer valid. We follow the approach suggested by Engle and Ng ( 1993) which artificially nests the GARCH and EGARCH models. Once both models are estimated in a nested specification, likelihood ratio tests are then applied again. Maximum likelihood function values derived from the artificially nested models and related ratio tests are reported in Table 4. The best model for each exchange rate is reported in Table 4 as we11.6 In the pre-EMS subperiod, the best fit models are variants of EGARCH models. with majority of the currencies follow an AR( 5)-EGARCH(4, 4)model, that is, the autoregressive process with exponential GARCH errors. The best model for the Dutch guilder, the Greek drachma and the Portuguese escudo is the exponential GARCH(4, 4) model without an autoregressive process. In the EMS subperiod the results are quite similar. The best model for all rates is either an EGARCH(p, 4) or an AR(S)-EGARCH(p, q)model, except for the Dutch guilder where an AR( 1 ))GARCH( 1, 1) specification fits best. Our likelihood ratio tests suggest that the improvement in maximum likelihood functions is statistically significant. Overall. our results indicate that more elaborated models appear to fit EMS rates better. The estimated parameters for the best model of each exchange rate are given in Table 5 (pre-EMS subperiod) and Table 6 (EMS subperiod). These tables present the estimated parameters and their standard errors, the average conditional variance (Avg. Cond. Var.), and some diagnostic statistics on the standardized residuals. The main findings are summarized in the following. First of all, we find significant ARCH and GARCH coefficients for almost all rates for both periods. Our results confirm previous findings of ARCH/GARCH effects (Diebold and Pauly, 1988; Koutmos, 1994) in high-frequency exchange rates (daily or weekly). In addition, 4 parameters of the autoregressive process are also significant for most rates. This leads us to suggest that the characteristics of conditional means of EMS are quite different from other currencies which are most likely best described by a random walk process. Second, we find strong support for EGARCH models. The H parameters of the EGARCH(p, 4) model are mostly significant and have a correct sign. Since both the conditional and the unconditional means of EMS exchange rates show deprecia-

’ In linear regression models, it is expected that the full model will always have higher likelihood ratios due to the lower SSE. However, this is not necessarily true in a nonlinear model. The log-likelihood function depends on the standardized error term e,/(/z,)“‘. In some cases the full model actually has lower likelihood function value than the reduced model (even before the degree of freedom is adjusted for).

ANM Best model

ANM EGARCH LR-test: EGARCH

versus AR(5)EGARCH (4,4)

(4,4)

-373.98 26.26

AR(5)EGARCH

395.69 - 19.24

294.39 183.36

- 386.44 51.18

-360.85

386.07

(ANM) GARCH LR-test: GARCH

versus

(1) (7)

1979 to 30 October,

(4) (7)

14 March,

EGARCH

(4,4)

AR(5)EGARCH (494)

GARCH (LO

325.26 - 108.5

240.81 60.40

271.01

(3) (7)

AR(l)-

665.58 90.4

705.59 10.38

710.79

(3) (5)

(4,4) (4.4) 1991 (660 weekly observations)

AR(5)-

EGARCH

AR (5)EGARCH

(4.4)

EGARCH

140.09 - 12.98

143.15 12.46

-91.02 2.38

- 12.68

98.23 70.74

31.16

126.03 46.70

- 124.32 68.98

Best GARCH model Best EGARCH model Log-likelihood function value Artificially nested model

EMS subperiod:

(ANM) GARCH LR-test: GARCH versus ANM EGARCH LR-test: EGARCH versus ANM Best model

-36.84 79.48

133.60

149.38

-89.83

2.91

Artificially

nested model

(3) (7)

(3) (6)

(7)

1979 (218 weekly observations)

(1)

(4) (6)

(B/LFR)

(HFL)

( UKL)

(FF)

1975 to 8 March,

franc

Belg./Lux.

Dutch guilder

pound

models

(4.4)

EGARCH

217.17 - 146.64

143.00 1.70

(4.4)

EGARCH

AR(5)-

312.20 -46.9

82.76

241.37

288.75

(7)

143.85

(2)

(4,4)

AR( 5)EGARCH

286.56 - 140.96

256.64 -81.12

2 16.08

(4) (7)

(474)

(4.4)

(2)

AR(5)EGARCH

-42.7

-92.96

- 124.32 20.02

- 114.31

(7)

(1)

(IRL)

punt

Irish

AR(5)EGARCH

36.69 5.16

10.42 54.94

39.66

(7)

(1)

(DKR)

kroner

Danish

(6)

(4. 4)

AR(5)EGARCH

11.92

- 100.71

35.06

- 106.32

-88.79

(4) (7)

(LIT)

lira

Italian

and EGARCH

British

GARCH

franc

encompassing

French

ratio tests based on specifications

Pre-EMS subperiod: 8 January, Best GARCH model Best EGARCH model Log-likelihood function value

Table 4 Likelihood

(4.4)

AR(5)EGARCH

- 176.59 -415.9

-243.74 -281.60

- 384.54

(4) (7)

(4,4)

EGARCH

-69.49 -63.6

- 117.74 32.90

- 101.29

(3) (6)

(DRA)

drachma

Greek Spanish

(4,4)

EGARCH

-93.52 - 90.02

- 143.55 10.04

- 138.53

(4) (6)

(4. 4)

AR(5)EGARCH

- 258.05 -9.32

-311.42 97.42

-262.71

(7)

(1)

(PTA)

peseta

Portuguese

(4.4)

EGARCH

- 30.62 -228.56

- 165.73 -52.40

- 163.61

(2) (6)

(4.4)

EGARCH

- 265.98

- 30.62

- 165.73 4.23

- 163.61

(1) (6)

(ESC)

escudo

OJ226

-0.0269 0.2Mo 08205 584 49.02. -20362

-0.0579 04553 0.4065 447 2582 -288 I*

00357 -0.3m 13011 ,2.40.* 61.7V. -65.41

0.1034

-0.0158 0.0469 12448 11.22.* 382100 13871

0,117

0.8739..W22M) -0.3315 (0.332,) -0.0205 (0.3329) -0..,619'*(0IZW) 0.,6,4*'(0.1731, -0.0551 (0.,5,2, 0.2702'~(0095,) 0 1366

-02243*~~00610, 0.8343..(0.0520) -0.0591 (00439) -03432*'(0.055,) -0.2*2***,0.05,0, -0 7907'~~0034,~ 0.0389mo866) "9942

0,717

-5.73361*,I.M45) 09289.*(0.1904) 0.4796..(0.1709) -0.0444 (0.1223) 0.5271~(0.2402) -03176~0.2514) 0.02,3(0.0529) -0.9298.. (0.031,) -03901~02408) 0.4511.*(0.1653) 0,984

0.3262'~(0.0553) -0.0211 (0.0526) 0.0025(0.0351) OOBOJ (004%) 0.0694,0.0479)

0.016***(0.0%0)

Pre-EMS

-0.0110 0.22M 1.5292 19.54'. 30.66 -272.92

0.,4x

-O.M1,,0.1999) 03579** (0.1339) 0.3402~(0 1473) 0.3821**(0.,4,0) O.XW** (0.1742) -0.2632.. ~0.0671, -0.2459*.(00,24) -0.1655 (0.0846) 0.6703.'(0.0844) l.lO50~~,0.3737) 1.5314

0.1682**,0.03&) -0. ,252" (O.WO, -0.0718(0.0405) 0.0225(0.0391) -00J38,0.0(91) 0.0537co.0325,

errors in parentheses).

-3.1220**~1 1907) 0.5802" (0.1756) 01031 (02933)

-0.w70,0.035*)

0.0324~0.0185)

(standard

-06415~*~00354) 0.046,~O.OSJI) 0.2459..(00863)

-O.IW2*~(00392) -0,225** (Om96) 0.09Ov (0.0358)

-0.0102 (0.0188, cl.O112(0.0.472)

*Statistically significant at the 5% level. **Statistically significant at the 1% level.

"Cam SkKtiasu BJtnr LB(m) Log-L

reneuzr

-0.36\0(02678) 030,5**,0.1023) 0.3221saCOC666)

analysis

0.2430..(0.0270)

GARCH

"arianacequltloo -3.WI I*. (0.9306) 0731J*~~O0624) 1.1753..W991) I.302P (0.3518) 0.6725**~00*88) -1.1038*~(0.1064) -0.7*2Pa (0.247)

0.Ow2*~0.0388)

"llconditional O3cw "da"= StanddAd

‘4vcrnpc mnditiooal "lriance

14 B

wo 4, UI a, Q. 8s 8. 8,

;, +t 4, 4. 4,

Results of the univariate

Table 5

-0.0138 -0.2759 0.8864 560 44.5** - 162.02

03464

-\3399** (0,648) O.*S*9'*(0.0414) 0.3628**(0.107,) -0.1462~~ (0.0557) 03999**(0.0532) -o.eml** (O.Orn) -0.1**9*. (0.0445) -0.8123** (00613) -0.*14,** (0.0636) O.M0,** (0.0253) 0.4536

-0"579 0.4'53 0.4065 4.4, 2582 -2x* 18

07717

o.*l43*~(O0520) -0.0581 (0.0439) -63432.. (0.055,) -OL828*~,00570) -07907*~(0.0347, 0.0.,x9 ,0.0866) ow42

-0.6115'~(00354) 0.0167,O.OJSl) O.bi.59.' (0.0863) -0.?243*~(0.06,0)

-0 122P.(Ow96) O.Ot'E)6. (0.0358)

-0.1263 0.2841 2.6104 43.28.. 30.5100 -90.15

0.0043 -1.251s IO.4905 42.60*9 19.19 -267.33

0483,

0.8682

0.3,,0**(0.0818) -04904~~(0.0878) 1.9947

-0.5673'. (0.0216) -0.5356~*(0wO) -1.17C"P(O.0320) -,.ow,*'* (0.0601) 0.1241(0.11&o -0.,34,'* (0.0556) -0.1454~~ (0.0329) 0.,942**(0.01*4) 0.3049..(0.0539) -0.3773~~,00138) 1.5107

-o.o3w*

(O.a?42) 0.0512**(0.!m9) 0.Om9(0.0070,

-0.164*(0.156,) 0.851***(O.I518~ 0.5,42*.(0.1706) -0.2042(0.2265~ -0.2638 (0.2020, -0.6834*. (0.0762) -0.1692(0.0931, 0.2997..(0.1060)

(0.0192) (0.034,) -0 ,092’

0.0499**(O.cao5)

0.038W (Owd,) -0.0307~~w0079)

-0.0214 0.8752 3.5178 124 13.. 37.56 -2493,

0.3944

-2.6610(1.M25) -0.6421~1.xm) -0.646,(1.5025) -0.1684(1.5025) -0.5x9(1.5025) -1.3,80(1.5025) -1.4189 (1.50025~ -1035,(1.5025) -0.2223(,.5025) -0.8682 (1.125) I.4345

0.3703(1.5025)

1979 (218 weekly observations)

cl.2829~~ (0.036l~

1975 to 7 March,

(1IuO*~ (00270) -0.0102 (O.Ol*.s)

8 January,

l-J.M72**(0.0126, 0.1,W'(0.01,9, 0.0112,0.0472) -o.m,, 0.0122(0.0116) -0.0811*',0.0129)

subperiod:

analysis

(standard

0.0536 1.3776 9.1092 257.62.. 37.35 705.59

0.3702 2.0573 126.79.. 36.62 -372.96

I.0786 7.5669 ,646.97** M.78 -,I.34

* Statistically sgnificant at the 5% level. ** Statistically sgnificant at the 1% level.

-O.OLM

0.0900

1.1916

0.2x23**(0.0595) 0.0625(0.0939) -0.1333 (0.755) 0.7076**(0.0&82) -0.0162(0.%30) -0.1031" (0.0307) 0.5%9** (0.0311) -0.3926** (0.0563) -0.3527.' (0.1237) O.LOl2 1.27%

GARCH

0.2212

0.6199+*(0.2776) -0.@7Y)(O.2776) -0.3640(0.2776) 0.5031(0.2776) -0.1132(0.2776) 0.4964

0.0635(0.2776) 0.0129(0.2776) -0.4220 (0.2776)

Table 6 Results of the univariate

5.5577 1205.94** 64.55.' -242.62

0.9611

O.lS55

-0.29729.(0.0920) 0.5474*'(0.0946) l.l616~~(0.0677) 0.0506(0.0753) -l.W49** (0.0772) 0.5260..(0.0976) -0.0129 (0.0979) 0.2153

0.04% (Ois59)

-0.04% 1.3917 4.9ml 773.79** 37.03 -39253

0.21%

0X73, 35534 415.66" 27.11 316.79

0.1425

(OJ291)

(0.&40)

0.9149-

-0.0249 0.8Mo 5.0162 rlo.OI’* 56.45 -264.29

0.1714

0.0222 0.4292 1.55% 65.32.' 36.49 -762.*7

0.0397 1.1610 7.2697 1656.33*' 41.22 -113.17

0.5571

0.491~*(0.0797) -0.5520'.(0.01161) -03099"(0.05,l) -0.0126 (0.0513) -O.MlO(0.0709) 0.1%9** (0.0611) 1.2023

-0.1912*(0X967) -O.IUP (0.0633) -0.U75~*(0.0697) 0.5276**(0.0747) 0.3476**(0.0617) 0.1474(0.0621) 2.6636

0.771,

0251l..(0.&20) ' 0.5131**(0.0749) 0.7656**(0.%66)

0.35% 4.,544 m9.26** 47.40' -24933

0.0593

0.1633

-0.7m* (0.0691) -0.4654~*(o.wJ3) 0.14w* (0.0%9) um5** (0.0119) 0.2aw* (0.056,) -0.0%7** (0.0193) 13912

0.6361**(0.&32~ 0.1746**(0.0140) -01m*(O.0160)

1991 (660 weekly observations)

1.1835*'(0.%Gl) 0.5467**(0.0941) l.olOl**(0.0613)

1979 to 30 October,

-0.0402 (0.0250) (Oasso) -0.0153 (Om43) -0.0213 (0.0546) 0.1612**(0.0424) -0.3403'*(0.0%5) -0.0763(0!3779) -0.9964*'(0.0567) 0.6976**(0.0316) -0.061: iO.ca4) -0x66** (0.0779) 0.3647.tO.w.4) -0.2525**10.%26~ I.141(0.1319) 1.9096** 0.2635"(0.0192) 0.1749 0.3547

0.9292-

14 March,

o.mv* (0.0356)

EMS subperiod:

0.4762iLO655j -0.0422(1.4365) -0.0747 (1.2762) -0.6359 (l.5404) I.Ol64(1.4566) O.Yl3(1.56-32) -0.4636(1.6716) 0.4710~(0.2321) 0.2659

error in parentheses).

A4 Y. Hu et rd. i ht. Fin. Markets,

Inst. and Money 7 i 1997) 235-253

251

tion against mark on average, interventions aim at reversing the trend or forcing an appreciation versus the German mark are likely needed. Thus, a shock in the direction of further appreciation of the mark is likely to be viewed by the market as a negative signal, thus increases conditional volatility while a shock of the same magnitude in the opposite direction (the mark depreciated unexpectedly) is likely to reduce volatility. In our model, a positive Q should be consistent with the characteristics of the EMS. A closer look at our results shows that significant 0 coefficients are mostly positive, especially for those long-time EMS members. For the EMS period, the only two currencies with a negative Q are the British pound and the Portuguese escudo. The United Kingdom was part of EMS after October 1990. Portugal joined EMS after our sample period. Since the central banks of these two countries are not obliged to keep their currency movement within the band, it is not surprising that their currencies do not exhibit the same pattern as those of EMS currencies. Overall, an EGARCH model specification is well suited for capturing the correlation between returns and future conditional volatility. The ability of the EGARCH( p, q) specification to explain the exchange rates of a managed-float regime, such as the EMS may be due to the target-zone characteristics of the system that calls for special attention to model the directions of the shock. Whenever a bilateral (versus the German mark) exchange rate exhibits a high probability that it will eventually ‘pierce’ either the floor or the ceiling of the zone, the monetary authorities of the member states have to intervene in the foreign exchange markets. Their intervention aims at stabilizing the bilateral rate and bringing it closer to the central parity rate. Third, we examine whether volatility has decreased as a result of the establishment of the EMS and strengthened coordination among member countries. A comparison of average conditional variances in the pre-EMS and EMS periods reveals that volatility decreases for most of the currencies after the establishment of EMS. The exceptions are the British pound which is part of the EMS only for a very brief period of our sample, and the Belgium/Luxembourg franc and Greek drachma. The currencies from countries with high inflationary pressures tend to benefit the most from the EMS. For example, the lira’s volatility drops from 1.5314 to 0.2659. We also report the unconditional variances based on the parameters estimated. One of the advantages of an EGARCH model is that it does not need to impose nonnegativity constraints on the coefficients. The logarithm of the unconditional volatility can be computed as I%‘,/(1 -ES=, fij). A stationary volatility path requires that x7=1 Bj < 1.0. The unconditional variances for the pre- and post-EMS periods are calculated for all 10 currencies. During the pre-EMS period, the stationarity condition is violated in many cases. Nevertheless, the unconditional variances for all currencies satisfy the stationarity condition. Our results also suggest that the unconditional volatility decreased from the pre-EMS to post EMS period for all the currencies except the British pound and Spanish peseta. Using cP= 1 fii as a measure of volatility persistency we find that most of the currencies have a persistence measure far below unity, with the exception of the Portugal escudo. A close examination of the diagnostic statistics indicates that the standardized residuals are closer to normally distributed and very little autocorrelation is present for the pre-EMS period. On the contrary, in the EMS subperiod (Table 6) the

252

M. Y. Hu et al. 1 ht. Fin. Markets, Inst. and Money 7 (1997) 235-253

standardized residuals exhibit significant deviations from normality. Although kurtosis is greatly reduced, the diagnostic statistics continue to show significant deviations from normality for all models in the EMS period. McCurty and Morgan (1987) suggested that departures from conditional normality are likely to be associated with major policy events. By splitting our sample into pre- and post-EMS, considering the establishment of EMS as a major event, the kurtosis has been reduced greatly. However, the standardized residuals still fail to follow approximately the normal distribution. The significant deviations imply that other distributions may work out better to explain the log returns of the EMS exchange rates. The fact that previous studies (Hsieh, 1989) have used Student’s t-test and the log-normal distributions with little luck points toward the direction of other highly skewed distributions that may improve the fit of the models.

4. Conclusions The present study examines the performance of a number of alternative GARCH/EGARCH models during the pre-EMS and EMS periods. The empirical evidence provided in our study suggests that EGARCH specifications perform the best for all exchange rates in the pre-EMS subperiod and for most of them in the EMS subperiod. Moreover, we also find support that the EMS is effective in reducing the volatility (both conditional and unconditional) of most bilateral exchange rates. The EGARCH specifications are quite successful in explaining the exchange rate movements of a managed-float regime such as the EMS. In addition to providing evidence that is consistent with prior findings of asymmetric behavior of EMS rates (Koutmos, 1993; Kahya et al., 1994), we also attempt to explain why the asymmetry exist in the EMS rates. We argue that the different impact of unanticipated appreciation and depreciation on conditional volatility is due to the EMS arrangements. In addition to monitoring the volatility of currencies, the band imposed by the system calls for special attention to model the directions of the shock. Interventions by central banks which aim at stabilizing bilateral rates and bringing them closer to the central parity rates are mostly required when the successive shocks are large in magnitude and are in the same direction.

Acknowledgements The authors would like to thank Wayne Lee, an anonymous referee and the editor, Ike Mathur, for helpful suggestions and comments on our paper.

References Artis, M.J., 1990. The European Monetary System: a review of the research record. In: Bird, G. (Ed.), The International Financial Regime. Surrey University Press, UK.

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