Real exchange rate has proven to be an important factor in economy of a country therefore its volatility information is of importance to investors, policy makers, government and also other researchers. Exchange rates volatility has increase a lot of doubts in many economic sectors (industrial and agricultural) in Kenya.
This study modelled KSH/USD exchange rates thus discover the trend and characteristic of exchange rate volatility in Kenya for the period 2007-2016.The study used EGARCH model to explain the presence of exchange rate volatility and provide volatility forecast.
Its used forex data over the period 1st Jan 2007 to 1 st Jan 2016 to measure the volatility and analyze the exchanges rates changes over the specified period.
Time series plot for exchanges rates indicates the upwards trend of the Kenya shilling against the USA dollar. Other graphical representations, a case of ACF and PACF plots show presence of Autocorrelations in the exchange rate data. A set of parametric test were used to test stationary and normality of the exchange rates between the said periods.ADF test shown on stationary in the original exchange rates data and on doing first differencing stationary was achieved.
Studies conducted shows that EGARCH model overcomes the limitations of the symmetric GARCH models by accounting for the leverage effect and therefore EGARCH (1, 1) with normal distribution was the best empirically, based on the Akaike information criterion because it had smallest the AIC and loglikehood
TABLE OF CONTENT
LIST OF ABBREVIATIONS v
1. INTRODUCTION 10
1.1 Background of the Study 10
1.1.1 The concept of heteroskedasticity 11
1.1.2 Volatility of exchange rate definition 11
1.1.3 Evolution of the Foreign Exchange Markets in Kenya 12
1.1.4 Parametric measures 12
1.2 Statement of the Problem 12
1.3 Justification 13
1.4 Objectives of the Study 13
1.4.1 General Objectives 13
1.4.2 Specific Objective 14
1.5 Significance of Study 14
2. LITERATURE REVIEW 15
2.1 introduction 15
2.2 Previous Literature 15
3. METHODOLOGY 18
3.1 INTRODUCTION 18
3.2 THE GARCH MODEL 18
3.3 EGARCH MODEL 18
3.3.1 Parametric Measures 20
3.3.2 SKEWNESS 20
4.0 DATA ANALYSIS AND FINDINGS 21
4:1: DATA 21
4:2: EXPLORATORY DATA ANALYSIS 21
4:2:1 EXCHANGE RATES DATA 21
4.2.4. EXCHANGE RATES RETURN DATA 32
DESCRIPTIVE STATISTICS 32
4.3 EGARCH MODEL 39
5.0 CONCLUSION 44
5.1 Summary and Conclusion 44
This chapter entails the history and the nature of the Kenya exchange rate system. It also indicates the actual problem being studied and the far to which previous studies have done on , citing in particular the gaps which my study would attempt to address.
1.1 Background of the Study
Over many years, Kenyan shilling have enjoyed appreciable value against US dollar, this factor has created opportunities for rapid economic growth and stability after a successful movement from a fixed exchange rate to a crawling per regime in the early 1980s and finally to exchange rate system in 1990s. Domestic investors faces a lot risk as no one could predict the performance of the foreign exchange market. This situation also has an effect on importation and exportation level of the country. Kenya as a developing country striving to develop its agricultural and industrial base needs to improve its foreign exchange market to enable domestic investors export agricultural produce and import relevant Machineries, equipment’s and raw materials for the industrial consumption without uncertainties in the system. The increasing volatility of exchange rates after the fall of the Bretton Woods agreements has been a constant source of concern for both investors, policymakers and academician and we can recall how developed countries tried hard in the 1980s to limit US dollar volatility (one thinks of the Plaza and Louvre’s agreements, respectively in 1985 and 1987), and some European countries took a more radical and wiser decision by giving up their national currency for the euro in the year 1999.For developing countries, Kenya and the alike there is evidences of much more negative effects of the exchange rate volatility (Grier and Smallwood 2007) .Surprisingly, macroeconomic evidence of the effect of exchange-rate volatility on economy for instance, trade, and more generally on growth, has been quite unclear, pointing to minimal or insignificant effects. In that context, it seems quite disturbing to see a number of countries, specifically the developing ones, adopting more or less fixed exchange-rate systems, especially when one remembers the painful collapses of south-east Asian fixed pegs at the turn of the century.
The existence of well-developed financial markets should allow agents to deal appropriately on exchange-rate risk, thus eliminating its negative effects on major economic sectors as a case of foreign trading. In that sense, mitigation of exchange-rate risk is unlikely to be the main sources of the growth-enhancing effect of financial development found in the literature.
Economic fundamentals such as the inflation rate, interest rate and the balance of payments, which have been more volatile in the 1980s and early 1990s, by themselves, are sources of exchange rate volatility (Oz Turk, 2006). The NEWS impacts suggested by Tibesigwe and Kaberuka (2014) could also be added onto the list of the factors that bring about volatilities. In the exchange rates of any economy the volatilities in the macroeconomic variables have attracted most researchers to not only study the phenomenon but also suggest some remedies to this problem. This paper aims at using a different approach to the measure of volatility in exchange rate, which is parametric in nature and then analyses the trend which the exchange rate follow in responds to both negative and positive trends.
1.1.1 The concept of heteroskedasticity
In statistics, a sequences of random variables is heteroskedastic, if the random variables have different dispersions. The term means “differing variance” and come from Greek “hetero” (different) and “skedasis” (dispersion).when the standard deviations of a variable, monitored over a specific amount of time are non-constant. Heteroskedaticity is of two kinds. Conditional and unconditional.
Conditional heteroskedasticity identifies non constant when the future periods of high and low volatility can be identified.
1.1.2 Volatility of exchange rate definition
Volatility refers to the spread of all unlikely outcomes of an uncertain variable (Abdallah, 2011).
Exchange rate volatility is defined as the risk associated with the unexpected movement in the exchange rate(Oz Turk, 2006).
1.1.3 Evolution of the Foreign Exchange Markets in Kenya
The KES/USD exchange rate changed from fixed to crawling to floating eras between the year 1969 and 2009. Between 1966 and 1992, Kenya operated a ﬁxed exchange regime and the country had to frequently devalue its currency to reduce the negative eﬀects that real exchange rate volatility had on its economy (Munyoki et al., 2012)
The ﬂoating exchange rate system was adopted in 1993; however, there is no available evidence that success has been achieved in realizing the objective for which the foreign exchange market was liberalized (Munyoki et al. 2012)
1.1.4 Parametric measures
The parametric measure of exchange rate volatility on the other hand estimates volatility in exchange rate using the Exponential Generalized Autoregressive Conditional Heteroskedasticity (E-GARCH) model in this study. This is distinct from some past studies that employed the pure GARCH model to estimate exchange rate volatility. Literatures have given a number of advantages of the E-GARCH model over other methods of measuring volatility. For instance, first, E-GARCH automatically tests for ARCH effects in the series. Secondly, the model expresses explicitly the log of the conditional variance which implies that the leverage effect is exponential rather than quadratic, and that forecasts of the conditional variance are guaranteed to be nonnegative. The presence of leverage effect can be tested by the hypothesis that the impact is asymmetric
1.2 Statement of the Problem
The Kenya shilling has registered mixed performances against the USD. The ﬂuctuations ranged between 35 in 1994 when the Kenya shilling was strongest and 106 in 2016 when it was at its weakest. This has been a great hindrance to international transactions especially exportation of Agricultural products in Kenya. Several authors have therefore written on the extent to which the volatility in exchange rate has affected some basic macroeconomics factors which normally determine the directions of the working of the economy. Different approaches and methods of measuring exchange rate volatility have been used by different researchers over time leading to divergent results thus no consensus arrived at. This because there are no general ways of measuring volatility according to existing theories. Different statistical measures of exchange rate volatility have been proposed in the literature. However, two measures of volatility have widely been used in the literature which are the standard deviation method and a volatility measure generated from a generalized autoregressive conditional heteroscedasticity (GARCH) process. The standard deviation method has been criticized for simply assuming that the empirical distribution of the exchange rate is Gaussian and for ignoring the difference between predictable and unpredictable elements in the exchange rates process (Musonda, 2000; Hook and Boon, 2000).The GARCH method has two problems associated with it. Firstly, the non-negativity conditions of the variance may be violated by the estimated model. Secondly, the models cannot account for leverage effects, although they can account for volatility clustering and leptokurtosis (fat tails) in the series. Different economists use different models to measure exchange rate volatility (Orkhan, 2010). Orkhan (2010) however gives the list of various means of measuring volatility in the exchange rate and their users including the results.
The purpose of this paper therefore aims at using a different approach to the measure of volatility in exchange rate, which is parametric in nature and then analyses the trend which the exchange rate volatility has followed Kenyan exchange rate system.
1.4 Objectives of the Study
1.4.1 General Objectives
To model the volatility of exchange rates in Kenya.
1.4.2 Specific Objective
To fit an EGARCH model to KSH/DOLLAR.
1.5 Significance of the study
1. LITERATURE REVIEW
This chapter will elicit text of scholarly paper, which include the current knowledge including substantive findings, as well as theoretical and methodological contributions to this study done by other researchers.
2.2 Previous Literature
Over the last three decades that it is from 1980s to date, Researchers including Engle (1982), Bollerslev (1986) have done a lot in a number of time series models and improved the ARCH model to generate a more generalized ARCH model.
Tibesigwa and Kaberuka (2014) however, stated that though these models have been used in developed countries there is less applicability in the analysis of developing countries (third world countries) like Kenya. In one of the noticeable empirical studies done by Vergil (2002) where he did a study on the impact of real exchange rate volatility on the export flows of Turkey to the United States and its three major trading Partners in the European Union for the period between 1990 and 2000 found that the standard deviation of the percentage change in the exchange rate can be used to measure the exchange rate volatility.
Additionally, many authors (Christie, 1982; and Nelson, 1991) have cited out the evidence of asymmetric effects, suggesting the leverage effect relies on the direction of price changes.
In response to the weakness of symmetric assumption, Nelson (1991) brought out exponential GARCH (EGARCH) models with a conditional variance formulation that successfully captured asymmetric response in the conditional variance. EGARCH models have been demonstrated to be superior compare to other competing asymmetric conditional variance in many studies (Alexander (2009).
Another research done Alberg et al. (2006) to forecast performance of GARCH, EGARCH, GJR and APARCH models and found that the EGARCH model, which used a skewed Student-t distribution, produced significant results than any other model.
Latifa et al. (2013) come up with a research to model heteroscedasticity in foreign exchange for US, UK, Euro and Japanese Yen data based GARCH models. Monthly averages for the various currency exchange rates were collected for the period from January 2001 to December 2010, a total of 120 observations per foreign currency. The period was chosen because of the two major events that the country went through that is election period followed by the post-election violence in 2007/2008. Their major objective was to study how these election factor affected the performance of the said currencies.
Maana et al(2010) applied the GARCH model in the estimations of the volatility of the foreign exchange market in Kenya using the daily exchange rate data for, January 1993 to Dec 2002.Currencies used were USD, sterling pound, Euro and Japanese Yen. Data used was obtained from ember2006. The CBK archives .In is study of volatility in exchange rates, logarithm rates returns were used. Using the descriptive statistics for exchange rate returns, he found that skewness coefficients were greater than zero implying that the exchange returns distributions are not Gaussian.
Chipili (2006) states that, in spite of the importance of exchange rate volatility in macroeconomics he found that studies on kwacha exchange rate volatility has not been explored in developing countries, Zambia to be exact. The research was conducted over a longer sample period, 1964-2006 using relatively higher frequency data at monthly intervals. He employs both symmetric and asymmetric GARCH models.
Abdallah (2011) used daily observations from 19 Arab countries and considered the GARCH technique in modelling exchange rates. Observations in the period 1st January 2000 to 19th November 2011, a total of 4341, were used. The LM test was used to test for heteroscedasticity. GARCH model was then used to investigate the volatility clustering and persistence. EGARCH was used to capture leverage effects as GARCH models are poor in capturing these effects.
Sandoval (2006) studied the daily exchange rate data, from year 2000 to 2004, of seven Asian and developing Latin American countries, by employing the ARMA, GARCH, EGARCH and GJR- GARCH models for modeling the exchange rates. He founded out that, in the developing countries the absence of statistical significance between asymmetric and symmetric models was conditional to the application of in-sample and out-of-sample tests jointly.
Also, in an attempt to adopt a parametric measure of exchange rate volatility in Nigeria, Isitua and Neville (2006) investigated the effect of exchange rate volatility on trade flows in Nigeria. Their study employed the generalized autoregressive conditional heteroskedasticity (GARCH) technique to measure exchange rate volatility.
Furthermore the GARCH model has also been applied in research done by Danson et al. (2012) that analyzed the impact of real exchange rate volatility on economic growth in Kenya. Results depicted that exchange rate was very volatile for the entire period under study .These results imply the presence of the volatility periods in the most macroeconomic variables of the East African countries and therefore gives confidence in the a applicability of the GARCH model in capturing the volatility of these variables in the regional economies, he never captured the asymmetric effect.
The idea of the exhibition of the volatility periods in economic variables is also stressed by Oz Turk (2006) who in his paper confirms the existence of the volatility in trade brought about by shifts in the volatility of exchange rates who further suggests some critics of GARCH model.
In conclusion, a critical look at the findings of these various authors reveals that the degree of exchange rate volatility differs from one study to the other. This, of course, might be the reason why the findings of these studies on the effect of exchange rate volatility on a particular macroeconomic phenomenon, such as trade are not uniform given the fact that several researchers have ignored the degree of volatility in exchange rate among world Currencies. This paper adopts a more rigorous parametric measures of exchange rate volatility in Kenya using the Exponential Generalized Autoregressive Conditional Heteroskedasticity (E-GARCH) modelling technique which addresses the defects identified with GARCH model .
This chapter entails the methods to be used in order to gain perspective of the research study. The aims, research design, data collection and data analysis are discussed.
Daily forex data is used to study volatility of Kenya shilling over the United State Dollar. The data is dated 1st January 2007 to 1st Jan 2016 a total of 2302 sample observations obtain form http://www.centralbank.go.ke/index.php/rate-and-statistics/exchange-rates-2 . Mean values of daily exchange rate is the variable used to model volatility.
3.2 THE GARCH MODEL
The standard GARCH model allows the conditional variance to be dependent upon previous own lags. The basic structure of the symmetric normal GARCH model is GARCH (1, 1) given by Chris Brooks (2008)
Where denote the conditional variances.
The GARCH model above cannot account for leverage effect, does not allow for any feedback between the conditional Variance and mean and violates the non-negativity conditions. For these reason I opted to model the problem using asymmetric GARCH model called EGARCH.
The exponential generalized autoregressive conditional heteroskedasticity model (EGARCH) is one of the many forms of GARCH model by nelson (1991).We shall use EGARCH which has added benefit because it is expressed in terms of the log of conditional variance so that even if the parameters are negative, the conditional variance will always be positive thus we do not therefore have to artificially impose non-negativity constraints
Let be an identically and indeed sequence such that and
Then the conventional EGARCH model become
where are the coefficients to be estimate
Furthermore parameter represent a magnitude effect or the symmetric effect of the model. Measures the persistence in conditional volatility. The parameter measures the leverage effect. This parameter is important as it allows the EGARCH model to test for Asymmetrics.If then the model is symmetric when is greater than zero the positive shocks (good news) generate less volatility than negative shocks (bad news). When it implies that good news is more destabilizing than bad news. The EGARCH model used got a distinctive feature, i.e., conditional variance was modeled to capture the leverage effect of volatility.
The parameter measures the asymmetry or the leverage effect, the parameter of
importance so that the EGARCH model allows for testing of asymmetries. If , then the model is symmetric. When , then positive shocks (good news) generate less volatility than negative shocks (bad news).
4.0 DATA ANALYSIS AND FINDINGS
4:2: EXPLORATORY DATA ANALYSIS
4:2:1 EXCHANGE RATES DATA
Table of Descriptive statistics
Min 1st Qu Max 3st Qu medium mean
61.51 76.44 106.20 87.65 83.86 82.58
The times series plot of the forex data is as below in figure 4.1.
Say something about this plots
Figure 4.2 and figure 4.3 both showed that data isn’t normal but heavy tailed
The time series plot, figure 4.1, reveals that the time series is not stationary, we confirmed this plotting an Autocorrelation function plot figure 4.4.
Shapiro-Wilk normality test
W = 0.97204, p-value < 2.2e-16
The p –value is less than 0.05 imply that the data doesn’t follow normal distribution
It’s clearly that the original exchange rate data doesn’t come to zero as seen above in the ACF plot a significant prove that the series is not stationary.
We can confirmed this using the augmented dickey fuller test that the data is not stationary
ADF TEST FOR STATIONARITY
Dickey-Fuller = -2.9985, Lag order = 13, p-value = 0.1556
Alternative hypothesis: stationary
We accept the alternative hypothesis and conclude that the original exchange rate data is not stationary.
Test for ARCH effect
ARCH LM-test for arch effect
Test for arch effect
ARCH LM-test; Null hypothesis: no ARCH effects
Chi-squared = 2284.3, df = 12, p-value < 2.2e-16
We reject the null hypothesis and conclude the there is arch effect in the data thus Garch models is suitable.
To achieve stationary we need to difference the exchange rate data and also apply log transformation to stabilized the dispersion
Time series plot of the log transformation of exchange rate data.
The time series plot for the differenced series
The above time series plot roughly depicts that our data is now stationary after doing first differencing
Again it gives an idea that this forex data may not be identically and independent because the variance be constants over time, Volatility clustering is clearly evident.
We can see from the Augmented Dickey Fuller test that the differenced series is stationary
Augmented Dickey-Fuller Test
Dickey-Fuller = -11.343, Lag order = 13, p-value = 0.01
Alternative hypothesis: stationary
The p value is small and indication that our data is now stationary.
4.2.4. EXCHANGE RATES RETURN DATA
Table 4.3: Descriptive statistics of the USD/KES exchange rate return series
MEAN MIN MAX STANDARD DEV KURTOSIS SKEWNESS ADF
0.0001673 -0.0944600 0.0957800
0.004896149 75.87458 0.04612904 -11.089,0.01
From Table 4.3, the kurtosis and skewness explains that the exchange rate data is not normal.
The positive kurtosis tells us that the data is heavy tailed and the positive skewness reveal to us that the data is skewed to the right
Testing for stationary
The results of ADF test on exchange rates returns
Augmented Dickey-Fuller Test
Dickey-Fuller = -11.796, Lag order = 12, p-value = 0.01
Alternative hypothesis: stationary
The p value is so small therefore tells us that our returns series is stationary
To check for normality, we see the figure 4.7 below
Testing for ARCH effect
ARCH LM-test; Null hypothesis: no ARCH effects
Chi-squared = 18.887, df = 12, p-value = 0.09129
Figure 4.8 Give the heading here?? What is the figure for??
TEST FOR AUTOCORRELATION
ACF plot of the squared returns, figure 4.8 show adequate autocorrelations an indication that the daily rate returns aren’t independently and identically distributed.
Initially, ACF plot of the raw exchange rate data reveals serial correlation and the PACF plot of the
squared raw exchange rate series indicates long term dependence.
The presences of serial correlation, presence of ARCH effects and
long term dependence which are the assumption of the GARCH model are well satisfied
This model enables the conditional variance to be non-independent on its lags. The formal GARCH equations is
Garch model cannot account for asymmetric (leverage effect) thus EGARCH model an extension of GARCH was adopted in the study
4.3 EGARCH MODEL
Comparison of AIC and LogLikehood of Egarch (p, q) under conditional distribution
Normal Student skew-student
Mean Model : ARFIMA (0, 0, 0)
Distribution : norm
GARCH Model : eGARCH(1,1)
Mean Model : ARFIMA(0,0,0)
Distribution : std
Estimate Std. Error t value Pr(>|t|)
mu 0.000100 0.000033 3.0431 0.002342
ar1 0.137823 0.018464 7.4645 0.000000
omega -0.490195 0.152221 -3.2203 0.001281
alpha1 -0.034358 0.033068 -1.0390 0.298805
beta1 0.953523 0.015864 60.1046 0.000000
gamma1 0.594828 0.224707 2.6471 0.008118
skew 1.006216 0.019689 51.1056 0.000000
shape 2.331288 0.190051 12.2667 0.000000
Weighted Ljung-Box Test on Standardized Residuals
Lag 4.853 0.0275960
Lag[2*(p+q)+(p+q)-1] 5.101 0.0003461
Lag[4*(p+q)+(p+q)-1] 7.112 0.0174348
H0 : No serial correlation
From the table 4.7, Gamma is positive value of magnitude 0.248278 which reveals that the past positive events have more influenced on the future volatility. This coefficient shows the KES/USD volatility is higher after after shock (Bad news generate less volatility than good news).In financial market, depreciation of currency is usually followed by higher volatility but this is not the case for KES/USD exchange rates.
The sum, = 0.951455.This is less than one and indication that the volatility is persistence.
Therefor the model is
Weighted ARCH LM Tests
Statistic Shape Scale P-Value
ARCH Lag  0.006814 0.500 2.000 0.9342
ARCH Lag  0.020741 1.440 1.667 0.9986
ARCH Lag  0.028104 2.315 1.543 1.0000
5.0 CONCLUSION AND RECOMMENDATION
5.1 Summary and Conclusion
The study focused on the exchange rate returns volatility on the past 10 years looking critically on the periods of economic crisis 2008-2009.It evident that Kenyan currency exchange is greatly affected by periods of political turmoil, a case of 2007 post-election violence and this what attracted me to statistically check it through. EGARCH models was compared based on student t distribution, normal distribution and the skewed student t distributions. Evidence on non-normality of the exchange rate data was enough to conclude that the hypothesis that the data is normal was not valid. Further studies shows that GARCH modelling with leptokurtosis distribution have revealed that it can account for conditional heteroscedasticity and leptokurtosis but cannot accommodate for the well evident skewness in my sample data Because of the above crucial limitations of the GARCH model we opted for EGARCH, a GARCH family model to cover the limitations using the student t distributions as argued by rotich (2004) thus increased flexibility.
Empirical evidence are in support for the exponential GARCH model for the Traditional symmetric GARCH with normal distributions in estimating the model parameters.
Information on volatility of exchange rates is crucial to various groups such as importers, exporters, investors, policy makers, Governments etc. There is thus need to build models that can then be used forecasting. Facts about financial time series such as volatility clustering
and persistence were observed. Normality assumption was rejected in the original exchange rates data as well as in the residuals of the fitted model. This was inferred from the QQ-plots, histogram and the Shapiro test as well as the skewness and kurtosis coefficients. The chosen model with the skewed student-t distribution
was better suited to accommodate the skewness and kurtosis in the exchange rates return series.
This study opted for lower specifications of the GARCH models in spite of existence of higher orders reason being that then empirical evidence shows that the lower specifications are able to sufficiently capture the characteristics of exchange rates while at the same time upholding the principle of parsimony (Kocenda and Valachy, 2006)
Various GARCH and EGARCH(1,1)models were fitted with variations being made to the parameters of the mean used student t distribution .The volatility model on the other hand
was retained at (1,1) since many studies have shown that there is not much difference between higher order models so the GARCH(1,1) model is sufficient and obeys the principle of parsimony. The best fitting model was selected based on the lowest AIC and the highest log-likelihood. The resultant model was found to be EGARCH (1,1) with a student-t conditional distribution. Was the best.
The test for existence of asymmetry in the KES/USD was compelled by recent empirical evidence of strong support for its existence in foreign exchange markets (Firdmuc & Horvath, 2007). The EGARCH model provides a better fit than the GARCH model and its advantages over the GARCH model are the first, it can capture leverage effects and secondly, that there is no restriction that the parameters α1 and β1 must be positive. (Hansen and Lunde, 2005; Andersen Bollerslev, Chou and Kroner, 1992) are of a different opinion; that foreign exchange returns usually exhibit symmetric volatility unlike equity markets. They say that past positive and negative shocks have the same effects on future volatility. Bollerslev, Chou and Kroner (1992) argue that, ”whereas stock returns have been found to exhibit some degree of asymmetry, the two sided nature of foreign exchange markets makes such asymmetries less likely.”
For the KES/USD, the value of gamma is positive meaning that a positive shock has more impact on exchange rate volatility than a negative shock. This is in contrast to the leverage effects results in the developed countries. The EGARCH model was able to capture this. The EGARCH model was also found to be most suitable in the works of Miron et al.(2010), Zahangir et al.(2012 ), Ebral.(2013), Kamal et. al (2011) among others. In the Kenyan market, Rotich (2014) also found that the EGARCH(1,1) with student-t distribution was the best model for the KES/USD exchange rates . Spikes in volatility are observed at times when there is an appreciation of the KES/USD currency further confirming leverage effects.
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