Published on International Journal of Economics & Business
Publication Date: December, 2019
R. K. Avuglah, Adusei Bofa & E. Harris
Senior Lecturer, Department of Mathematics, KNUST
Lecturer, Department of Economics and Statistics, Garden City University College
Senior Lecturer, Department of Mathematics, KNUST
Convergence in macroeconomic variables amongst member countries is very vital and one of the main prerequisites for the West African Monetary Zone (WAMZ) to take oﬀ, hence this study focused on the changing aspects concerning exchange rates between the United States Dollars(US Dollar) vis-à-vis five currencies from the WAMZ. The currencies are the Ghanaian Cedi(GhCedi), Nigerian Naira(Naira), Gambian Dalasi(GMD), Guinean Franc(GNF) and Serra Leonean Leone(SSL), based on data availability from August 4, 2015 to May 7, 2019. We used the generalized orthogonal GARCH (GO-GARCH) to model the volatility among the WAMZ. Volatility is very likely to take a long time to end irrespective of no matter what happens in the market putting investors at risk in the short-term, hence negative effect on the economies. The outcomes communicate that all sample exchange rate series stand volatile. we conclude that volatility concept takes distinct significance concerning the framework of currency exchange rates. Investors and governments may implement dynamic investment strategies or regime based on current market shocks and long-run persistence in volatility markets in WAMZ. The government of respective nations must intervene through fiscal and monetary dealings to ensure stability in the exchange rate, as this will facilitate the economic integration of the zone.
Keywords: GO-GARCH, WAMZ, MGARCH, volatility, Exchange Rate.
Concerning international trade the foreign exchange market is very crucial, as numerous world economies remain indirectly or directly linked through export and import trades. As a result of high reliance of African countries on foreign exchange, complete monetary integration is vital however it has been lugged in the glare of exchange rate risk. Convergence in macroeconomic variables amongst member countries is very vital and one of the main prerequisites for the West African Monetary Zone (WAMZ) to take oﬀ. The capacities of countries in the WAMZ to meet the convergence measures looks unlikely. In view of the WAMZ not able to reach convergence in exchange rates and other macroeconomic fundamentals since its inception, makes the study of the changing aspects concerning exchange rates a very pertinent undertaking for policy-making in the sub-region (Seck,2014). Also, the evidence of exchange rate volatility spillover between WAMZ countries would offer a basis for foreign portfolio investors and international traders to come up with effective approaches for hedging against exchange rate shocks that are distributed among countries by designing suitable risk management practices.
A growing literature exists on exchange rate volatility concerning West Africa (see e.g. Adeoye and Atanda, 2011; Merreh et al., 2014). Olowe (2009) studied the log-returns volatility of the average Naira/Dollar exchange rates by means of TS-GARCH (1, 1), IGARCH (1, 1), APARCH (1, 1), EGARCH (1, 1), GJR-GARCH (1, 1)and GARCH (1, 1) ) models using monthly historical data spanning the period January 1970 to December 2007. Other works likened exchange rates volatility between few West Africa nations (see e.g. Omojimite and Akpokodje, 2010; Onanuga and Onanuga, 2015; Tchokote et al., 2015).
In modeling exchange rates volatilities each of the studies cited above used univariate GARCH-type models, and few others compared conditional variance estimates across exchange rates. But then when attention is concerned on modeling the joint development of a system of time series and want to exploit the covariance between both series. These models turn out to be inadequate and required to be extended to a multivariate framework. As a result, this study used a variant MGARCH model (the GO-GARCH), intending to understand the dynamics of the conditional correlation of exchange volatilities in the WAMZ.
2.1 Multivariate GARCH Models
Quite a lot of works dealt with univariate GARCH models, nevertheless interaction between markets now and then, needed to use the MGARCH models, which remained defined as:
At time t is defined as vector of a stochastic process, an vector of conditional mean, an vector of shocks, or innovation of the series at time t. To remodel the series at time t is defined as matrix of conditional variances of , at time t, is a vector of iid error such that where an identity matrix of order n.
2.2 The Generalized Orthogonal-GARCH (GO- GARCH) model
The GO-GARCH model has the assumption that the vector observed process is defined by an n-vector of a linear combination of n conditionally uncorrelated factors or components (Isenah and Olubusoye,2016).
From equation 2 above W was the linear map that links uncorrelated components or factors utilizing the observed variables was assumed to be constant over time, besides invertible. W was decomposed into an orthogonal matrix U and is a symmetric positive fixed matrix. Then 3
From equation 3 the symmetric positive definite square root of the unconditional covariance matrix Σ was defined (Boswijk and Weide, 2011)
As an alternative to equation 4
Where A and B represented the matrices with, correspondingly, the orthogonal eigenvectors plus the eigenvalues of Σ= . U is the orthogonal matrix of eigenvectors of A and B would estimate directly by way of unconditional information (Weide, 2002).
The components or factors may well be stated as:
Where ) was an diagonal matrix of conditional variances, the random vector process as the characteristics . Hence, the conditional covariance matrix of
As considered by van der Weide the were assumed to have was to assume separate univariate GARCH (1,1):
2.3 Fast Independent Component Analysis (Fast-ICA) estimator
In the estimation of GO-GARCH model, Broda and Paolella (2008) presented a two-step algorithm called CHICAGO (Conditionally Heteroscedastic Independent Component Analysis of Generalized Orthogonal GARCH models). The CHICAGO process used independent component analysis as a device for the breakdown of a high-dimensional problem into a set of univariate models. The conditional heteroscedasticity of the estimated components or factors is maximized by the ICA procedure.
Ghalanos(2015) and Isenah and Olubusoye(2016) summarized the algorithm for estimation as follows. Foremost, the Fast-ICA was applied to the whitened data where was found as of the eigenvalue decomposition of the OLS residuals covariance matrix. Next, the conditional log-likelihood function was uttered utilizing the totality of the individual conditional loglikelihoods, resulting from the conditional marginal densities of the factors or components, such, , in addition to a term for the matrix W, which is estimated in the first step through Fast- ICA:
Where remains a vector of unknown parameters in the marginal densities.
The historical data set obtained from Bloomberg comprised daily exchange rates of the United States Dollars(US Dollar) vis-à-vis five currencies from the WAMZ. The currencies are the Ghanaian Cedi(GhCedi), Nigerian Naira(Naira), Gambian Dalasi(GMD), Guinean Franc(GNF) and Serra Leonean Leone(SSL)(Liberia excluded). Based on data availability exchange rate from August 4, 2015 to May 7,2019 . The descriptive statistics summary for the currencies (Table 1) show that all the selected currencies have a coefficient of skewness different from 0 (they are all positive excluding Ghanaian Cedi and Serra Leonean Leone). However, the kurtosis values are very small, suggesting that our sample currencies are platykurtic which is consistent by means of rejection of the null hypothesis of the normal distribution, as shown by the small probability values of the Jarque–Berra test of normality 5% significance level. The Ghanaian Cedi was less volatile whereas Serra Leonean Leone was more volatile than the others based on the magnitude of the unconditional standard deviations. Table 2 reports the unconditional correlation matrix among currencies. The Ghcedi currency is more highly correlated with one another ranging from 0.61 to 0.89.
Figure 1 presented the daily exchange rate series between the US Dollar and the five currencies from the WAMZ (GhCedi, Naira, GMD, GNF, SSL). Concerning volatility clustering figure 1 confirms that which makes multivariate GARCH model suitable for analyzing the data. Can it be that the WAMZ countries’ experience the same exchange rate vitality concerning the US Dollars? The answer is provided by the modeling exchange rate with the GO-GARCH.
Figure1: Exchange rate series for total of 953 daily observations.
Table 1: Descriptive statistics for exchange rate
Statistics Ghanaian Cedi Gambian Dalasi Guinean Franc Nigerian Naira Serra Leonean Leone
Mean 4.361832 45.2465 8789.705914 306.766917 656451
Median 4.435 47.25 9046.82 359.645 4364
St. Deviation 0.441144 3.458095 628.074296 65.207094 1603.663202
Skewness 0.5755892 -0.3625701 -1.3402054 -0.8538618 1.1131466
Kurtosis -0.1887655 -0.05338879 0.02896459 -0.0935551 -0.45913795
Maximum 5.855 50.330 9449.220 367.500 8949.097
Minimum 3.705 38.830 7250.010 197.00 3701.000
Obsevation 953 953 953 953 953
Table 2: Unconditional correlation matrix among the five currencies
GhCedi GMD GNF Naira SSL
GhCedi 1.0000000 0.8900102 0.6104609 0.7813260 0.8120077
GMD 1.0000000 0.7099599 0.8851413 0.6850917
GNF 1.0000000 0.8506978 0.3457797
Naira 0.8506978 1.0000000 0.4979213
4. The GO-GARCH Model for Exchange Rate
The results presented in table 3 show coefficients of the GO-GARCH model with Log-Likelihood -19659.54. The estimated parameters showed that the factors presented volatility clustering since α+ β remains close to 1 for all factors. Concerning the short-term persistence coefficient on the α term for the five currencies, the Naira was with the lowest value whereas the SSL was with the highest. Again, regarding the long-term persistence, the Naira had the highest and the SSL remains the least. Excluding the Naira, the short-term persistence was less than the long-term persistence for all the currencies. The estimated coefficients values of α and β are positive and sum value (α + β < 1), explaining that the shocks to volatility do have an identical magnitude in these markets. The relatively large coefficient of ARCH effect indicates that conditional volatility does change quickly which may be due to the macroeconomic uncertainty of the WAMZ. Concerning the large size of GARCH effect, the conditional volatility series tend not to fluctuate gradually over time showing the persistence of shocks. Investors and governments may implement dynamic investment strategies or regime based on current market shocks and long-run persistence in volatility markets in WAMZ. From figure 2 below the time-varying plots of the conditional correlations likewise, display periods of high volatilities in the co-movements of the exchange rates. Regarding the pair-wise conditional correlations coefficients between the five currencies increase and remain fairly stable towards the end of the sample, except for those between the GhCedi & Naira, GMD & SSL, and SSL and Naira which appear to decrease toward the end. Table 3: Coefficient estimation of GO-GARCH Coefficients Ghanaian Cedi Gambian Dalasi Guinean Franc Nigerian Naira Serra Leonean Leone omega 0.00964537 0.003525659 0.007511102 0.002430526 0.01284603 alpha1 0.571382027 0.653316186 0.501273849 0.457980354 0.61848169 beta1 0.427617846 0.345683733 0.497726149 0.541019361 0.32108552 Orthogonal Matrix(U) among the five currencies GhCedi GMD GNF Naira SSL GhCedi -0.722 0.297 -0.1336 -0.603 0.097 GMD -0.109 -0.839 -0.331 -0.196 0.495 GNF -0.201 -0.209 0.8680 -0.116 -0.386 Naira 0.135 -0.346 -0.4231 -0.379 -0.730 SSL -0.635 -0.213 -0.2206 0.664 -0.251 Notes: U shows the rotation matrix. No standard errors estimated because of GO-GARCH factors estimates. Figure 2: The Pair-Wise Conditional Correlation All the currencies in the WAMZ are volatility sensitive to the market events as this is consistent with the relatively large α values marking the WAMZ very volatile in relation to the US Dollar. Volatility is very likely to take long time to end irrespective of no matter what happening in the market putting investors at risk in the short-term, hence negative effect on the economies. the Orthogonal Matrix U for our model is presented in table 4. 5. Conclusion Empirical evidence analyzed in this work advocates that all the WAMZ countries’ currencies experience exchange rate volatility clustering with regards to the US Dollars however not of matching level. The difference in the degree of volatility exchange rate perhaps may be due to the domestic economy getting unstable source(s) of foreign earnings or growing level of craving for trade in goods in the respective nations among others. The government of respective nations must intervene through fiscal and monetary dealings to ensure stability in the exchange rate, as this will facilitate the economic integration of the zone. Since the widely held important conditions have remained achieved through increased access to information and communication technology and trade facilitation, Monetary powers that be in the zone should muster the political push to enable the WAMZ converge to full financial integration. Exchange rate volatility dynamics should equally consider by traders and international investors in making buy-or-sale and other investment or speculation decisions. Investors should be proactive in scheming effective approaches for hedging in contrast to exchange rate volatility dynamics information from any of these currencies. 6. References Alexios Ghalanos, (2015), The rmgarch models: Background and properties, from http://cran.rproject.org/web/packages/rmgarch/vignettes/The_rmgarch_models. Adeoye, B.W. and Atanda, A.A. (2011), “Exchange rate volatility in Nigeria: consistency, persistency & severity analyses”, CBN Journal of Applied Statistics, Vol. 2 No. 2, pp. 29-49. Godknows M. 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