Modelling Exchange Rate Volatility of Somali Shilling Against US Dollar by Utilizing GARCH Models

Abstract

The main aim of this investigation was to model the volatility of Somali shilling against US dollar by using monthly data covering from 1950 to 2010. Further to that, this finding has adopted both symmetric and asymmetric generalized autoregressive conditional heteroscedastic (GARCH) family models in order to capture volatility clustering and leverage effect as the most stylized facts of exchange rate returns. Result from ARCH indicates presence of conditional heteroscedasticity in the residual series of exchange rate. Symmetric GARCH(1,1) model shows presence of volatility clustering and persistent coefficients of greater than one indicating that volatility is an explosive process. Results from asymmetric TCHARCH(1,1) and EGARCH(1,1) indicates presence of leverage effect in the series of exchange rate where positive news have large effect on volatility than bad news of same magnitude. This study has an important implication to investors, business and risk managers. Nevertheless, this study suggest monetary authority to print new currency and de-dollarize the economy in order to be able influence exchange rate volatility. The outcome from this finding also suggests that GARCH family models sufficiently capture the volatility of Somali shilling against US dollar.

Full text

International Journal of Economics and Financial
Issues
ISSN: 2146-4138
available at http: www.econjournals.com
International Journal of Economics and Financial Issues, 2021, 11(2), 35-39.
International Journal of Economics and Financial Issues | Vol 11 • Issue 2 • 2021 35
Modelling Exchange Rate Volatility of Somali Shilling Against US
Dollar by Utilizing GARCH Models
Abdullahi Osman Ali*
Puntland Ministry of Finance, Garowe, Somalia. *Email: ccciglami2@gmail.com
Received: 14 April 2020 Accepted: 25 December 2020 DOI: https://doi.org/10.32479/ije.9788
ABSTRACT
The main aim of this investigation was to model the volatility of Somali shilling against US dollar by using monthly data covering from 1950 to 2010.
Further to that, this nding has adopted both symmetric and asymmetric generalized autoregressive conditional heteroscedastic (GARCH) family models
in order to capture volatility clustering and leverage eect as the most stylized facts of exchange rate returns. Result from ARCH indicates presence
of conditional heteroscedasticity in the residual series of exchange rate. Symmetric GARCH(1,1) model shows presence of volatility clustering and
persistent coecients of <1 indicating that volatility is an explosive process. Results from asymmetric TCHARCH(1,1) and EGARCH(1,1) indicates
presence of leverage eect in the series of exchange rate meaning positive news have large eect on volatility than bad news of same magnitude.
This study has an important implication to investors and risk managers. Nevertheless, this study suggests monetary authority to print new currency
and de-dollarize the economy in order to be able inuence exchange rate volatility. The outcome from this nding also suggests that GARCH family
models suciently capture the volatility of Somali shilling against US dollar.
Keywords: Exchange Rate, Somali Shilling, US Dollar, Conditional Heteroscedasticity, Volatility Clustering and Leverage Eect
JEL Classications: F31, O24
1. INTRODUCTION
Exchange rate is the rate at which one currency is converted
or exchanged into another. Therefore, there are two categories
of exchange rate regime in which every country has to adopt
a particular one. The rst one is oating exchange rate regime
where a value of a currency is allowed to uctuate against other
currencies in response of market forces. The Other category is
pegged exchange rate which is also know xed exchange rate,
this type the value of a certain currency is xed against either
basket of another currencies or any other measure of value such
as gold.
After the end of Bretton wood monetary system decisions
regarding which exchange regime to apply become more
challenging in this modern economy as trade and capital markets
become more integrated in the world as stated by (Berg and
Borensztein, 2001). Despite that exchange rate has gained much
attention due to its strong link with most of the macroeconomic
variables. (Bahmani‐Oskooee and Mohammadian, 2016) study
showed that exchange rate volatility aects domestic production,
therefore following this work exchange rate will gain attention as
any country want make policy concerning domestic production.
Further to that, there are signicant relationship among exchange
rate and macroeconomic variables as conrmed by (Su, 2012).
Therefore, following this evidence exchange rate become an
important element in macroeconomic analysis and economic
decision making.
Since oating exchange rate become prominent across the world
countries after the end of Bretton wood system modelling exchange
rate by measuring its uctuation (risk) become vital. (Abdalla,
2012) conducted nding to model exchange rate of nineteen Arab
countries while using GARCH models nd out the existence
This Journal is licensed under a Creative Commons Attribution 4.0 International License

Ali: Modelling Exchange Rate Volatility of Somali Shilling Against US Dollar by Utilizing GARCH Models
International Journal of Economics and Financial Issues | Vol 11 • Issue 2 • 2021
36
leverage eect which indicates that negative eect have large
eect on volatility than positive change of same magnitude. There
is presence of volatility clustering and leverage eect on USD
against Kenyan shilling as conrmed by the work of (Omari et al.,
2017). (Epaphra, 2016) nd that current exchange rate volatility
depends on its previous uctuation and presence of leverage
eect although positive shocks have more eect on volatility than
negative shocks of same size as he elaborated by using Tanzania
shilling against USD. Both (Abdalla, 2012; Mohsin, 2018) of
these investigation nd the presence of leverage eect where
negative shocks have greater inuence on volatility than positives
shocks. Despite of the research outcome all of the cited ndings
has adopted GARCH models.
Somali economy is characterized by high dollarization and
unregulated exchange rate as the central bank of the nation
become ineective due to collapse of Somali republic back in
1991. Moreover, no study has considered modelling time series
data of S.SH against USD apart from the work of (Nor et al.,
2020) which focused macroeconomic determinants of exchange
rate. therefore this study ll this gap by modelling exchange rate
(S.SH/USD) while adopting GARCH model due to its relevant in
capturing volatility as applied by almost all the ndings regarding
this matter.
Although Somalia’s economy is highly dollarized economy,
there are still the use of Somali shilling in the market. However
the biggest and smallest is 1000 Somali shilling which can easily
faked in other way supplied in the market illegally by individuals
as conrmed by (Yusuf and Abdurrahman, 2019).
2. DATA AND METHODOLOGY
2.1. Data
In order to model volatility of exchange rate (SOS/USD) as the
research objective of this investigation, this article deployed
monthly exchange rate of Somali shilling against US dollar data
covering period from 1950 to 2010. Further to that time series data
of exchange rate (SOS/USD) was sourced from Federal Reserve
Bank of St. Louis.
2.2. Methodology
2.2.1. Unit root test
Most macroeconomic and nancial time series are reect trending
which is indication of non-stationary. As non-stationary time series
analysis lead ordinary least square (OLS) procedures to produce
misleading or incorrect results (spurious regression). To avoid the
problem of spurious regression this nding conducted united root
test by deploying Augmented dickey-fuller test using developed
by (Dickey and Fuller, 1979).

yyy
ttt
i
k
it t
 





01
1
1
where yt stands for shows the tested time series, t is the sign of
time trend, ∆ stands for change of rst dierence and k is the lag
order of the autoregressive process.
The null hypothesis (H0) which says there is unit root or the
exchange rate series is not stationary is reject and alternative
hypothesis (H1) is accepted if the t-statistic is greater the critical
value as stated by (Dickey and Fuller, 1979).
2.2.2. Modelling volatility
To model volatility of exchange rate (SOS/USG) this study adopts
ARCH and GARCH family models to ensure if large changes is
followed by large change and small changes is followed by small
changes (volatility clustering).
2.2.3. GARCH family models
GARCH family models are splitted in to symmetric and
asymmetric. Conditional variance depends on the magnitude of
the change rather than the sign in symmetric models while changes
of same magnitude have dierent eect on future volatility under
asymmetric models.
GARCH and GARCH-in-Mean are considered to be symmetric
models of GARCH family. as far as this study is concerned
GARCH model will be focused. Autoregressive conditionally
heteroscedastic (ARCH) was first developed by (Engle,
1982) and after that Generalized Autoregressive Conditional
Heteroscedasticity (GARCH) model by (Bollerslev, 1986).
Ordinary least square (OLS) regression assumes that variance of
error term is constant (homoscedasticity) although it is not the
case of nancial time series which exhibit non constant variance
(heteroscedasticity). In this case the existence of heretoscedastic in
SOS/USD series leads autoregressive conditionally heteroscedastic
(ARCH) model for the variance of errors. ARCH model was rst
developed by (Engle, 1982) by stating that the variance of residuals
at time t depends squared residuals of error time in the past periods.
Therefore by allowing the dependence of variance on lagged period
of squared residuals (Engle, 1982) specied as follows:


tt
u
2
01
1
2


If test statistic (TxR2/the number of observations multiplied by
the coecient of multiple correlation) is signicant we reject
the null hypothesis of homoscedasticity (variance of error term
is constant) and conclude that ARCH eects are present. In the
instance where ARCH eects are present in SOS/USD series we
proceed to check volatility clustering by adopting GARCH model.
As stated by (Narsoo, 2015) it is dicult to signicantly capture
the dynamic behaviour of volatility by ARCH model demands
high ARCH order. Bollerslev’s model GARCH dealt the weakness
by allowing the conditional variance to depend its own previous
lags. GARCH(1,1) which similar to ARIMA(1,1) can be specied
in general form as:
 

t
i
q
it
i
q
jtj
u
2
0
1
1
2
1
2
 





Where:
σ
t
2
stands for the estimated conditional variance.

Ali: Modelling Exchange Rate Volatility of Somali Shilling Against US Dollar by Utilizing GARCH Models
International Journal of Economics and Financial Issues | Vol 11 • Issue 2 • 2021 37
ut−
1
2 stands for the past squared residuals.
2
tj
σ
− lagged conditional variance.
Generalized autoregressive conditional heteroscedasticity
(GARCH) model is considered to be more parsimonious and
less likely to breach non-negativity compared to autoregressive
conditional heteroscedasticity (ARCH) as stated Model by
(Bollerslev, 1986).
After GARCH model was developed, various extension and
variants has been proposed considering to asymmetric models and
most prominent are GARCH-M, TGARCH and EGARCH models.
In addition to that these asymmetric models was developed as
symmetric models violated non-negativity constraints and cannot
account for leverage eect as conrmed by (Narsoo, 2015). From
the asymmetric models this nding will only consider TGARCH
and EGARCH.
Threshold generalized autoregressive conditional heteroscedasticity
(TGARCH) model introduces multiplicative dummy variable in
to the variance equation to check if positive and negative shocks
of same magnitude have dierent eect on volatility. Further to
that TGARCH model is specied as:
hy hyuud
ttttt
 

01111
2
1
2
1

Where d takes the value of 1 for ut < 0 and 0 otherwise.
So good news has an impact of y while bad news has an impact of
y + θ. If θ > 0 we conclude that there is asymmetry while if θ = 0
we say the news is symmetric.
The variance equation of exponential Generalized autoregressive
conditional heteroscedasticity (EGARCH) developed by (Nelson,
1991) is specied as:
loglog

tt
t
t
t
t
uu
2
1
21
1
2
1
1
2
2



 













Even if the parameters are negative,
σ
t
2
will be positive because
since we model the
lo
g

t
2

.
3. EMPIRICAL RESULT AND DISCUSSION
3.1. Descriptive Statistics and Unit Root Test
The information presented in table shows that the mean of
exchange rate is positive. As presented in Table 1 the skewness
of 1.8 indicates that exchange rate has long right tail with positive
skewness. Since the kurtosis of 6, 2 is greater than standard
univariate normal distribution of 3 the exchange rate series is
leptokurtic which means the distribution graph of exchange rate
(SOS/USD) high and thin. Since P-value of Jarque-Bera test is
<1% signicant level we reject the null hypothesis of normal
distribution which indicates that SOS/USD series is not normally
distributed.
This investigation adopted Augmented dickey-fuller unit root test
to ensure the stationarity of exchange rate series. As presented in
Table 2 exchange rate series is not stationary at level. Therefore
to transform the SOS/USD time series date into stationary this is
done by dierentiating twice EXRATE as indicated in Table 3
meaning exchange rate is integrated order one I(2). T-statistic
of augment dickey fuller is less than the critical values at 1%
signicance level we reject the null hypothesis that there is unit
root and conclude that SOS/USD series is now stationary at I(2).
In this case we can proceed to test the presence of ARCH eect
in exchange rate series.
3.2. Heteroskedasticity Test
The result presented in Table 4 shows that P-value of 0.0000 is
<5% signicance level we reject the null hypothesis no ARCH
eect. This means existence of ARCH eect in exchange rate
(S.SH/USD) series. In the present case this nding will estimate
ARCH family models.
The exchange rate of Somalia shilling against US dollar was
regulated by monetary authority but after the collapse of Somali
state in 1991 the system remains unregulated until date. As
Figure 1 presents exchange rate seems variable stable from 1950
till 1987 but right after that S.SH/USD was getting more volatile
and reected volatility clustering.
Table 1: Summary statistics of exchange rate (S.SH/USD)
Mean 4004.881
Median 7.142860
Maximum 31900.00
Minimum 6.281500
Std. Dev. 6921.123
Skewness 1.887834
Kurtosis 6.215822
Sum 2931573.
Sum Sq. dev. 3.50E+10
Observations 732
Jarque-Bera 750.2140
Probability 0.000000
Table 2: Augmented dickey-fuller test of EXRATE
(S.SH/USD)
t-statistic Prob.*
Augmented Dickey-Fuller test statistic 1.551456 0.9994
Test critical values: 1% level −3.439217
5% level −2.865344
10% level −2.568852
Table 3: Augmented dickey-fuller unit root test of
DEXRATE
t-statistic Prob.
Augmented Dickey-Fuller test statistic −26.54391 0.0000
Test critical values: 1% level −3.439217
5% level −2.865344
10% level −2.568852
Table 4: Heteroskedasticity test: ARCH
F-statistic 58.17523 Prob. F(1,726) 0.0000
Obs*R-squared 54.00778 Prob. Chi-square(1) 0.0000

Ali: Modelling Exchange Rate Volatility of Somali Shilling Against US Dollar by Utilizing GARCH Models
International Journal of Economics and Financial Issues | Vol 11 • Issue 2 • 2021
38
3.3. Estimation Results of GARCH, TGARCH and
EGARCH
Results from GARCH(1,1) in Table 5 shows that coecients
both ARCH (b) and GARCH (α) are positive except Constant
(ω) which is negative but all the three coecients are statistically
signicant at 1% signicance level. The signicance of α reveals
the presence of volatility clust3ering in GARCH(1,1). The value
of α + ∝ (persistence volatility shocks) which is <1 suggest that
conditional variance is an explosive process meaning that the eect
of today’s shock remains in the forecast of variance for numerous
periods in the future.
The result from TGARCH(1,1) presented in Table 5 indicates
that the coecient of asymmetry is positive and signicant at
1% signicance level which means presence of asymmetry in
exchange rate series therefore there is dierence of 0.4 between
bad and good news. In this case modelling the news is signicant
determinant of exchange rate volatility. Moreover, as the result
of EGARCH(1,1) in Table 5 illustrates the coecient of leverage
eect is positive and signicant at 5% which indicates that good
news have larger eect on volatility of SOS/USD series than
bad news of same magnitude. The implication of this result is
that good news (appreciation of SOS/USD) creates more risk in
the market compared to bad new (depreciation of SOS/USD).
This happens because Somalia’s economy is heavily dollarized
as banks only accept dollar as a currency and daily transactions
heavily involve US dollar. When Somali shilling depreciates
people, banks, companies and businesses with huge amount of
dollar than Somali shilling will encounter exchange rate risk
and through that way appreciation of SOS/USD create more
risk in the market.
4. CONCLUSION
This study adopted GARCH, TGARCH and EGARCH model with
the intention to model Somali shilling against US dollar while
monthly time series data covering period from January 1950 to
December 2010.
The result from this investigation nd that SOS/USD is not
normally distributed and presence of autoregressive in conditional
heteroscedasticity in the residual series. Result from GARCH
indicates existence of ARCH eect in the residual series and
volatility clustering as well. The result from TGARCH showed
signicant presence dierence between good and bad news of
same magnitude (asymmetry) while the outcome from EGARCH
model reveals presence of leverage eect which indicating that
positive news have large eect on volatility then bad news of
same magnitude.
The ndings from this study provide a relevant implication
concerning market timing, portfolio selection and measuring risk
to investor and risk managers in Somalia. despite of that this study
suggest to investor and business owners to pay close attention to
exchange rate risk and set better risk management strategies to deal
with exchange rate risk. Further to that, this nding recommend to
government of Somalia to introduce new currency and de-dollarize
the economy to be able to inuence exchange rate uctuation
and transform. Lastly, this article concludes that GARCH family
models suciently capture the volatility of Somali shilling against
US dollar.
5. ACKNOWLEDGEMENT
I prepared this work with curiosity without getting fund from any
agency. I acknowledge that this work lls a real gap as this nding
is about modelling the volatility of Somali shilling against US
dollar which is not considered by any other study prior.
REFERENCES
Abdalla, S.Z.S. (2012), Modelling exchange rate volatility using GARCH
models: Empirical evidence from Arab countries. International
Journal of Economics and Finance, 4(3), 216-229.
Bahmani-Oskooee, M., Mohammadian, A. (2016), Asymmetry eects
of exchange rate changes on domestic production: Evidence from
nonlinear ARDL approach. Australian Economic Papers, 55(3),
181-191.
Berg, A., Borensztein, E. (2001), Full Dollarization: The Pros and Cons.
Table 5: Results of GARCH, TGARCH AND EGARCH
Model GARCH (1,1) TGARCH (1,1) EGARCH (1,1)
Variable Coecient Prob. Coecient Prob. Coecient Prob.
Constant (Ꞷ) −0.0000157 0.0000 −0.0000399 0.0000 6.282103 0.0000
ARCH eect (ꞵ) 0.290290 0.0000 0.038938 0.0086 0.512478 0.0000
Leverage eect (γ) ------------- -------- -------------- ------- 0.122238 0.0484
Symmetry (threshold) ------------- -------- 0.401645 0.0000 ---------------- ------
GARCH eect (α) 0.997125 0.0000 0.997776 0.0000 0.168591 0.0005
DLEXRATE −0.526345 0.0004 −0.550733 0.0000 −0.362912 0.0000
Log likelihood −1910.700 −1928.219 −5728.825
Figure 1: exchange rate (S.SH/USD) volatility

Ali: Modelling Exchange Rate Volatility of Somali Shilling Against US Dollar by Utilizing GARCH Models
International Journal of Economics and Financial Issues | Vol 11 • Issue 2 • 2021 39
Washington, DC: International Monetary Fund.
Bollerslev, T. (1986), Generalized autoregressive conditional
heteroskedasticity. Journal of Econometrics, 31(3), 307-327.
Dickey, D.A., Fuller, W.A. (1979), Autoregressive time series with a
unit root. Journal of the American Statistical Association, 74(366),
427-431.
Engle, R.F. (1982) Autoregressive conditional heteroscedasticity with
estimates of the variance of United Kingdom ination. Econometrica:
Journal of the Econometric Society, 1982, 987-1007.
Epaphra, M. (2016), Modeling exchange rate volatility: Application of the
GARCH and EGARCH models. Journal of Mathematical Finance,
7(1), 121-143.
Mohsin, M. (2018) Modeling exchange rate volatility using garch models:
Empirical evidence from Pakistan. European Journal of Research,
1(2), 73-88.
Narsoo, J. (2015), Forecasting USD/MUR exchange rate dynamics: An
application of asymmetric volatility models. International Journal
of Statistics and Applications, 5(5), 247-256.
Nelson, D.B. (1991), Conditional heteroskedasticity in asset returns: A
new approach. Econometrica: Journal of the Econometric Society,
59, 347-370.
Nor, M.I., Masron, T.A., Alabdullah, T.T.Y. (2020), Macroeconomic
fundamentals and the exchange rate volatility: Empirical evidence
from somalia. SAGE Open, 10(1), 2158244019898841.
Omari, C.O., Mwita, P.N., Waititu, A.G. (2017), Modeling USD/KES
exchange rate volatility using GARCH models. IOSR Journal of
Economics and Finance, 8(1), 2321-5933.
Su, C.W. (2012), The relationship between exchange rate and
macroeconomic variables in China. Zbornik radova Ekonomskog
fakulteta u Rijeci: Časopis za Ekonomsku Teoriju i Praksu, 30(1),
33-56.
Yusuf, A.N., Abdurrahman, O. (2019), The devastating local currency and
the unocial dollarization in Somalia. Fiscaoeconomia, 3(3), 42-57.