VOLATILITY OF STOCK PRICES IN TANZANIA: APPLICATION OF GARCH MODELS TO DAR ES SALAAM STOCK EXCHANGE
^{1}Department of Economics, the Open University of Tanzania Dar es salaam, Tanzania.
^{2}Treasury Square Building 18 Jakaya Kikwete Road, Dodoma, Tanzania.
ABSTRACT
We use Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models to examine volatility of stock prices for firms listed in the Dar es Salaam Stock Exchange (DSE). In doing so, both symmetric and asymmetric GARCH models are used in this study. The descriptive analysis of the data shows that standard deviation of the series returns is high, indicating a high level of daily fluctuations, and the log value of the mean is close to zero. Our empirical results clearly exhibit evidence of volatility and volatility clustering, a typical feature of financial time series. Moreover, our results indicate that the series are highly leptokurtic, flat tailed and asymmetric consistent with characteristics of financial time series data. Out of all models examined, EGARCH (1,1) and GARCH (1,1) seem to perform plausibly better than others.
Keywords:Volatility, Dar es Salaam, Stock Exchange, Share Price Index, ARCH, GARCH, Tanzania.
JEL Classification:G17; C12; C13.
ARTICLE HISTORY: Received: 5 November 2020, Revised: 1 December 2020, Accepted: 23 December 2020, Published:14 January 2021
Contribution/ Originality: This study contributes to the existing literature through the application of both GARCH and the EGARCH models in order to capture both symmetry and asymmetry effects, and determines key characteristics of stock returns at Dar es salaam Stock Exchange.
This paper attempts to model volatility of stock prices in Dar es salaam Stock Exchange (DSE) in Tanzania for the period between January 2014 and November 2019. The motivation for undertaking this exercise is two folds. First, although much has been documented on the volatility of stock prices elsewhere in the world, relatively little is known in the context of Tanzania (see for example, (Achal, Girish, Ranjit, & Bishal, 2015; Ajaya & Swagatika, 2018; Akhtar & Khan, 2016; Mathur, Chotia, & Rao, 2016)). Existing studies that have attempted to examine volatility within the context of GARCH models in Tanzania have mainly focused on other macroeconomic variables such as inflation (Edward, Eliab, & Estomih, 2004) exchange rate (Carolyn, Betuel, & Pitos, 2018; Epaphra, 2016) tax revenues (Chimilila, 2017). Secondly, while there exists a paucity of research in this area, it remains indisputable that traders in the stock exchange need reasonable understanding of stock volatility and forecasts on future values of stock prices. Since volatility of stock price may hike transaction costs and reduce the gains to traders in the financial markets, it suffices to argue that knowledge of stock price volatility estimation and forecasting is extremely imperative for asset pricing and risk management (Srinivasan & Ibrahim, 2010).
Over the last three decades or so, volatility modeling has been a subject of rigorous empirical investigation, pioneered by Eagle (1982); Domowitz and Hakkio (1985) and Bollerslev (1986). The Autoregressive Conditional Heteroscedasticity (ARCH) model by Engle takes into consideration differences between conditional and unconditional variance, and in doing so, it allows for unconditional variance to change overtime as a function of past disturbance terms. GARCH, on the other hand, allows for a more flexible of lag structure that permits a more parsimonious description in many economic situation. The GARCH models are oftentimes preferred by researchers in financial modelling because they provide a more realworld context than other forms when trying to predict stock prices. In short, GARCH model involves three steps. The first step is to estimate a bestfitting autoregressive model. The second step is to compute and plot the autocorrelations of the disturbance term. Third, is to test for significance whereby the null hypothesis states that there are no ARCH or GARCH errors. Numerous extensions of the GARCH model have been developed in the literature, and it is the major preoccupation of this paper to examine them in our analysis.
Our estimated results show that a null hypothesis of no ARCH effect is strongly rejected since the pvalue is less that 5 percent level of significance, suggesting the presence of ARCH effect in the data series. We also find that our data series have heteroscedastic characteristics and therefore support use of GARCH models. The weighted average of Akaike Information Criterion (AIC) and Schwarz Information criterion (SIC) of the selected GARCH shows that EGARCH (1, 1) has the lowest values of AIC and SIC followed by the GARCH (1, 1) model respectively. A correlogram of Standardized Residuals Squared shows that the null hypothesis of no serial correlation is accepted for both models. The Jarque Bera test of normality in the residuals is accepted at five percent level of significance showing that residuals are normally distributed. And lastly, the forecast of the two models show an evidence of volatility in returns, and a low value of Root Mean Square Error (0.0093) for both GARCH (1,1) and EGARCH indicates the two models are reasonably accurate.
We contribute to the literature in two major dimensions. First, unlike the relatively few previous studies done in Tanzania (see for example, Mutaju and Dickson (2019)), we apply both GARCH and the EGARCH models to capture both symmetry and asymmetry effects, and determine key characteristics of DSE stock returns. Secondly, unlike Mutaju and Dickson (2019) we divide our data set into three periods, namely; the period between 2014 and 2019, the period before "General Election" (20142015) and after "General Election" of 2015 (20162019). We believe this categorization of period is important because change of power by those in government may influence investor's participation in the stock market through the adoption of "wait and see" attitude (Nancy, 2016) and this might have remarkable consequences on the behavior of stock prices. Our results, nevertheless, are not susceptible to the effects of "General Election" of 2015.
The remainder of this study is organized as follows. Section 2 reviews briefly empirical literature. Section 3 spells out model specification. Section 4 reports and discusses the empirical results. Section 5 concludes.
On the empirical front, numerous studies have empirically applied the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) developed by Bollerslev (1986). Aktan, Korsakienė, and Smaliukienė (2010) examine Baltic Stock Markets comprising of Estonia, Latvia and Lithuania using a broad range of GARCH volatility models. The study tested GARCH models that include basic GARCH model, GARCHinmean model, asymmetric exponential GARCH, GJR GARCH, power GARCH and component GARCH model in Baltic Stock Markets comprising of Estonia, Latvia and Lithuania; and found a strong evidence that daily returns are bettermodelled using GARCHtype models, though did not specify a bestfit model.
Srinivasan and Ibrahim (2010) attempted to forecast conditional variance of the SENSEX Index returns of Indian Stock Market using daily data from January 1996 to January 2010 and found that symmetric GARCH models perform better in forecasting conditional variance rather than the asymmetric GARCH models, despite the presence of leverage effect. Though the paper provides substantial empirical evidence of the characteristics of BSE30 index, it did not undertake rigorous discussion of the literature cited.
Ahmed and Suliman (2011) on the other hand, used the symmetric and asymmetric GARCH model to estimate volatility in the daily returns of Khartoum Stock Exchange (KSE) over the period from January 2006 to November 2010. The study found that conditional variance process is highly persistent and provide evidence of the existence of risk premium for the KSE index return series; which supported the positive correlation hypothesis between volatility and the expected stock returns. Although this study successfully compared symmetric and asymmetric GARCH models in the context of KSE, did not specify the bestfit model for the KSE return series. On the other hand, Prateek (2015) undertook a robust comparison of the daily conditional variance forecasts of seven GARCHfamily models using daily price observations of 21 stock indices of the world for the period 1 January 2000 to 30 November 2013. The study found that standard GARCH model outperforms the more advanced GARCH models and provides the best onestepahead forecasts of the daily conditional variance. The study did not undertake modelfitting tests to confirm the models.
Ajaya and Swagatika (2018) measured return volatility and dynamic conditional correlation between the stock markets of North America region using weekly stock market returns data from January 1995 to June 2016. Using univariate ARCH and GARCH approaches, the study found an evidence of return volatility and its persistence within the region. Further, as expected, emerging markets are less linked to the developed market in terms of return and there exists weak linkage between the stock markets; and there is no evidence of market integration throughout the sample period. Though the study provides substantial empirical work to benchmark stock markets of the North American region, the study could go further to capture characteristics of the stock markets with reference to any asymmetric model such as EGARCH.
In the context of Tanzania, Mutaju and Dickson (2019) attempted to model volatility of stock returns at Dar es Salaam Stock Exchange (DSE) using daily closing stock price indices from 2nd January 2012 to 22nd November 2018. Both symmetrical and asymmetrical Generalized Autoregressive Heteroskedastic Models, namely, GARCH (1,1), EGARCH (1,1) and PGARCH (1,1), were employed. The findings revealed that all three models were statistically significant to forecast stock returns volatility. Our paper differs from Mutaju and Dickson (2019) in that it examines the characteristics of the stock returns on three subperiods, as has been mentioned above, namely, from January 2014November 2019; January 2014December 2015 (election period) and from January 2016November, 2019. Secondly, we compare the best model based on AIC, SIC and log likelihood estimators as opposed to Mutaju and Dickson (2019) which compared the forecasting accuracy of the models. Third, unlike Mutaju and Dickson (2019) this paper performs a battery of diagnostic tests to check for serial correlation, normality and presence of ARCH effect in the selected models. Fourth, our work is based on recent data and therefore reveals more accurate returns conditions to stock investors.
The ARCH model developed by Eagle (1982) is used to model conditional variance.
GARCH model (Bollerslev, 1986) is an extension of ARCH model developed by Eagle (1982). In the GARCH model, previous days variances are used to forecast future variance given by the following conditional variance equation:
The EGARCH model captures response of timevarying variance to shock, and at the same time ensures the variance is positive (Ayele, Gabreyohannes, & Tesfay, 2017). An EGARCH with order (p, q) is given by the following equation:
Empirically, it has been demonstrated that bad news has a greater impact on volatility than good news of the same magnitude.
We develop the variance equation based on the model defined by Ayele et al 2017 as follows:
In this paper, daily returns were calculated as the continuously compounded returns, which are first difference in logarithm of closing all share prices, using the following formula:
The index is a weighted index based on market capitalization where the weight of any company is taken as the number of ordinary shares listed in the market. The index allows the price movements of larger companies to have a greater impact on the index.
The first step before applying GARCH models is to test for the presence of ARCH effect. Both Figure 1 (a) of the series trend and Figure 1 (b) of plotted residuals show that periods of high volatility are followed by periods of low volatility.
Figure1(a). Plot of Index Return: January 2014November 2019.
Figure1(b). Plot of Index Return: January 2014December 2015.
Figure1(c). Plot of Index Return: January 2016December 2015.
January 2014 November 2019 (A) 
January 2014December 2015 (B) 
January 2016November 2019 (C) 

Mean 
0.0000209 
0.000202 
0.0000713 
Median 
0.0000 
0.000326 
0.0000 
Maximum 
0.070817 
0.033080 
0.070817 
Minimum 
0.072202 
0.021125 
0.072202 
Std. Dev. 
0.009280 
0.004544 
0.010931 
Variance 
0.000086 
0.0000206 
0.000121 
Skewness 
0.008730 
0.778077 
0.041303 
Kurtosis 
27.43288 
10.82 
21.3592 
JarqueBera 
36,414.9 
1308.86 
13623.18 
Probability 
0.0000 
0.00000 
0.0000 
Sum 
0.030610 
0.099780 
0.069170 
Sum Sq. Dev. 
0.125985 
0.010179 
0.115782 
Observations 
1464 
494 
970 
The descriptive analysis shows series A and C have small positive mean; whereas series B has a positive mean. The daily variance and volatility intensity for Series A, B and C are 0.000086, 0.0000206 and 0.000121with series A showing highest volatility followed by series A and B. The high kurtosis values of 27.4, 10.8 and 21.4 indicate that the returns are leptokurtic, flat tailed; asymmetric and do not follow normal distribution. Series A and B are positively skewed, and Series C is negatively skewed. The standard deviation is found to be high, indicating a high level of daily fluctuation of DSE returns. The mean return is close to zero as expected for return series (Srinivasan & Ibrahim, 2010). The mean log return is negative for series A and B, and is positive for series C during postelection period.
As shown in Table 2, the Augmented Dickey Fuller (ADF) Unit Root test rejects a null hypothesis of presence of unit root for the time series, suggesting that the series are stationary at level and hence mean reverting. This is important in order to ensure model stability.
Critical Values 

ADF Statistics 
Probability 
1% 
5% 
10% 

Index return (Series A)  39.680 
0.000 
3.435 
2.863 
2.568 
Index return (Series B)  13.687 
0.000 
3.443 
2.867 
2.569 
Index return (Series C)  25.542 
0.000 
3.437 
2.864 
2.568 
As shown in Table 3, the null hypothesis of no ARCH effect is rejected since the pvalue is less that 5 percent level of significance, implying presence of ARCH effect in the data series. The time series have heteroscedastic characteristics and therefore support use of GARCH models.
Series Name  FStatistic 
Observed Rsquared 
Probability ChiSquare 
Index return (Series A)  190.044 
302.239 (0.000) 
0.000 
Index return (Series B)  10.780 
10.59168 (0.001) 
0.001 
Index return (Series C)  241.2237 
193.5018 (0.000) 
0.000 
The weighted average of AIC, SIC of the selected GARCH shows that EGARCH (1, 1) has the lowest values of AIC and SIC followed by the GARCH (1, 1) model respectively. The log likelihood values of the two models are highest, as shown in Table 4:
January 2014December 2019 (A)  January 2014December 2015 (B) 
January 2016November 2019 (C) 

AIC 
SIC 
LL* 
AIC 
SIC 
LL* 
AIC 
SIC 
LL* 

EGARCH  7.439 
7.421 
5450.3 
8.039 
7.997 
1990.8 
7.225 
7.195 
3510.3 
GARCH (1,1)  7.441 
7.426 
5450.3 
8.027 
7.993 
1986.7 
7.202 
7.177 
3498.2 
TARCH (GJR GARCH)  7.444 
7.426 
5454.1 
8.026 
7.983 
1987.4 
7.204 
7.173 
3499.7 
PARCH  7.443 
7.422 
5454.8 
8.026 
7.975 
1988.4 
7.209 
7.179 
3502.8 
IGARCH  7.357 
7.349 
5387.2 
7.859 
7.842 
1943.1 
7.124 
7.109 
3458.2 
Note: 1. LL*: Log Likelihood 2. By definition AIC = 2 log (likelihood)+2T and BIC = 2 log (likelihood)+log (Tk), where T denotes the number of observations used for the estimation of parameters, and k is the number of (free) parameters in the model. Given a set of candidate models, the model with the minimum AIC and BIC value is taken as the bestfit model. 
The weighted average results for these models show that DSE is successfully modeled using EGARCH and GARCH (1,1) since they have slightly lowest aggregated values of AIC and SIC, and highest log likelihood. Interestingly, all models analyzed have slightly small difference in terms of the AIC, SIC and Log Likelihood and all of them were statistically significant. Of these two models, EGARCH is superior followed by the GARCH (1, 1). To understand the key characteristics of these models, we closely examine them to show their applicability to DSE return series.
In this section, we determine the significance of coefficients of the mean and variance equation for GARCH (1, 1) for all the three periods. The results are indicated in Table 5.
Mean Equation 
Variance Equation 

Coefficient 
zstatistic 
Coefficient 
zstatistic 
Probability 

Constant 
0.000184 
0.52869 
α 
0.00000261 (0.000000214) 
12.18812 
0.000 
0.243241 (0.0014048) 
17.3151 
0.000 

0.745101 (0.012016) 
62.00722 
0.000 
Mean Equation 
Variance Equation 

Coefficient 
zstatistic 
Coefficient 
zstatistic 
Probability 

Constant 
0.000326 (0.000188) 
1.737587 
α 
7.89E05 (8.64E06) 
9.124816 
0.000 
0.269757(0.034662) 
7.782584 
0.000 

0.015152(0.076123) 
0.199044 
0.000 
Mean Equation 
Variance Equation 

Coefficient 
zstatistic 
Coefficient 
zstatistic 
Probability 

Constant 
8.71E06 (0.000359) 
0.024290 
α 
0.000000654 (6.90E08) 
9.4806 
0.000 
0.139710 (0.008344) 
16.74303 
0.000 

0.875796 (0.003532) 
247.9364 
0.000 
Table 5(a)(c) show that the coefficients of variance equations are statistically significant. All coefficients of the variance equation meet the conditions of the GARCH (1,1) model, their sum being less than 1. Table 5 (a) for Series A indicate that the volatility of returns is quite persistent, with the sum of α and β being 0.99; implying a volatility halflife of about 173 days. In other words, this indicates that lagged conditional variance and squared disturbance have an impact on the conditional variance: news about volatility from the previous periods has an explanatory power on current volatility. On the other hand, Series B has less persistency of 0.27, which shows a high decay to long run variance, and halflife of a half day. We therefore conclude that the returns volatility of these two series are mean reverting as the sum of α and β is signiﬁcantly less than one. Series C has a persistence greater than one and thus indicates that the shocks to the conditional variance are highly persistent, i.e. the conditional variance process is explosive.
The positive value indicates that good news increases the future volatility more than the bad news, which is consistent with the findings of Joldes (2019).
Variable 
Coefficient 
Std. Error 
zStatistic 
Probability 
C 
0.000373 
0.000268 
1.390717 
0.000 
Variance Equation 

0.542044 
0.025326 
21.40252 
0.0000 

0.355020 
0.013950 
25.44983 
0.0000 

0.025447 
0.009759 
2.607449 
0.0091 

0.963298 
0.002548 
378.0911 
0.0000 
Variable 
Coefficient 
Std. Error 
zStatistic 
Prob. 
C 
0.0000429 
0.000228 
1.882400 
0.0598 
Variance Equation 

0.674113 
0.035257 
19.12012 
0.0000 

0.368690 
0.015049 
24.49887 
0.0000 

0.037905 
0.010149 
3.735031 
0.0002 

0.957325 
0.003035 
315.4411 
0.0000 
Variable 
Coefficient 
Std. Error 
zStatistic 
Prob. 
C 
04.75E05 
0.000386 
0.123260 
0.9019 
Variance Equation 

7.28E07 
7.45E08 
9.771344 
0.0000 

0.173547 
0.015167 
11.44266 
0.0000 

0.066541 
0.021353 
3.116305 
0.0018 

0.873867 
0.003746 
233.2594 
0.0000 
In order to investigate whether the two models fulfill the best fit conditions, a correlogram of Standardized Residuals Squared test is used to find out whether the two models are serially correlated or not. The null hypothesis of no serial correlation is accepted for both models since the pvalues are greater than five percent, which is a desirable condition (see Appendix 1 (a)(b)). Then, the models are tested to check whether they have ARCH effect: the null hypothesis of no ARCH effect is accepted at five percent level of significance since both pvalues are greater than five percent Table 7. Lastly, as required, the Jarque Bera test of normality in the residuals is accepted at five percent level of significance showing that residuals are normally distributed [see Appendix 2 (a)(f)]. Therefore, we empirically show that both GARCH (1, 1) and EGARCH models have fulfilled all conditions of bestfit models, and can be used to describe and model DSE ASI returns. As shown in appendix 3, the forecast of the two models shows an evidence of volatility in returns, and a low value of Root Mean Square Error (0.0093) for both GARCH (1,1) and EGARCH indicates the two models have forecasting power and are accurate.
FStatistic 
Probability 
Obs*Rsquared 
Prob. ChiSquare(36 

Series A 
0.472349 
Prob. F(36,1391) (0.9968) 
17.24605 
0.9965 
Series B 
0.890099 
Prob. F(36,421) (0.6541) 
32.39411 
0.6408 
Series C 
0.506892 
Prob. F(36,897) (0.9934) 
0.9934 
0.9926 
This study has attempted to undertake empirical investigation of DSE allshare price returns and using (GARCH (1,1), EGARCH, TGARCH, PGARCH and component GARCH; using a sample size of 1465 observations from 02 January 2014 to 28 November, 2019. We can safely conclude the following: firstly, the ASI returns are volatile and demonstrate volatility clustering, which is a key characteristic underlying financial time series. Secondly, the series demonstrate ARCH effect supporting use of GARCH models. Third, the ASI returns are stationary at level, which is a desirable condition for our analysis. Fourth, the ASI return is normally distributed and is highly leptokurtosis as seen from the high kurtosis values discussed above. Fifth, the EGARCH model for Series A and B has positive leverage effect, unlike Series C which has negative leverage effect meaning bad news has an impact on volatility more than good news. Of all models, GARCH (1,1) and EGARCH models are superior with the lowest AIC and SIC and largest log likelihood values followed by the PARCH model. We empirically show presence of return volatility and persistence in the return series analyzed; and that lagged conditional variance and squared residuals have an impact on the conditional variance. The two models passed a battery of diagnostic test in order to check the bestfit.
Funding: This study received no specific financial support. 
Competing Interests: The authors declare that they have no competing interests. 
Acknowledgement: Both authors contributed equally to the conception and design of the study. 
Achal, L., ., Girish, K. J., Ranjit, K. P., & Bishal, G. (2015). Modelling and forecasting of price volatility: An application of GARCH and EGARCH models. Agricultural Economics Research Review, 28(1), 7382.Available at: https://doi.org/10.5958/09740279.2015.00005.1.
Ahmed, A. E. M., & Suliman, S. Z. (2011). Modeling stock market volatility using GARCH models evidence from Sudan. International Journal of Business and Social Science, 2(23), 114128.
Ajaya, K. P., & Swagatika, N. (2018). A GARCH modelling of volatility and MGARCH approach of stock market linkages of North America. Global Business Review, 19(6), 15381553.Available at: https://doi.org/10.1177/0972150918793554.
Akhtar, S., & Khan, N. (2016). Modeling volatility on the Karachi stock exchange, Pakistan. Journal of Asia Business Studies, 10(3), 253275.
Aktan, B., Korsakienė, R., & Smaliukienė, R. (2010). Timevarying volatility modeling of baltic stock markets. Journal of Business Economics and Management, 11(3), 511–532.
Ayele, A. W., Gabreyohannes, E., & Tesfay, Y. Y. (2017). Macroeconomic determinants of volatility for the gold price in Ethiopia: The application of GARCH and EWMA volatility models. Global Business Review, 18(2), 308326.Available at: https://doi.org/10.1177/0972150916668601.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31(3), 307327.Available at: https://doi.org/10.1016/03044076(86)900631.
Carolyn, O., Betuel, C., & Pitos, B. (2018). Modeling exchange rate volatility using APARCH Models. Journal of the Institute of Engineering, 14(1), 96106.
Chimilila, C. (2017). Forecasting tax revenue and its volatility in Tanzania. African Journal of Economic Review, 5(1), 84109.
Domowitz, I., & Hakkio, C. (1985). Conditional variance and the risk premium in the foreign exchange market. Journal of International Economics, 19(12), 4766.
Eagle, R. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom Inflation. Econometrica, 50(4), 9871007.
Edward, N., Eliab, L., & Estomih, S. M. (2004). Time series modelling with application to Tanzania Inflation Data. Journal of Data Analysis and Information Processing, 2(2), 4959.
Epaphra, M. (2016). Modeling exchange rate volatility: Application of the GARCH and EGARCH models. Journal of Mathematical Finance, 7(1), 121143.Available at: https://doi.org/10.4236/jmf.2017.71007.
Joldes, C. C. (2019). Modeling the volatility of the bucharest stock exchange using GARCH Models. Economic Computation and Economic Cybernetics Studies and Research, 53(1), 281298.Available at: https://doi.org/10.24818/18423264/53.1.19.18.
Mathur, S., Chotia, V., & Rao, N. (2016). Modelling the impact of global financial crisis on the Indian stock market through GARCH models. AsiaPacific Journal of Management Research and Innovation, 12(1), 1122.
Mutaju, M., & Dickson, P. (2019). Modeling stock market volatility using GARCH models case study of dar es salaam stock exchange (DSE). Review of Integrative Business and Economics Research, 9(2), 138149.
Nancy, S. (2016). Waitand see: Investment options under policy uncertainty. Review of Economic Dynamics, 21, 246265.Available at: https://doi.org/10.1016/j.red.2015.06.001.
Prateek, S. (2015). Forecasting stock index volatility with GARCH models: International evidence. Studies in Economics and Finance, 32(4), 445463.
Srinivasan, P., & Ibrahim, P. (2010). Forecasting stock market volatility of bse30 Index Using GARCH Models. Asia Pacific Business Review, 6(3), 47–60.
Autocorrelation 
Partial Correlation 
AC 
PAC 
QStat 
Prob* 

  
  
1 
0.029 
0.029 
1.1976 
0.274 
  
  
2 
0.009 
0.008 
1.3079 
0.520 
  
  
3 
0.020 
0.020 
1.8706 
0.600 
  
  
4 
0.003 
0.004 
1.8856 
0.757 
  
  
5 
0.014 
0.014 
2.1582 
0.827 
  
  
6 
0.015 
0.015 
2.4914 
0.869 
  
  
7 
0.009 
0.007 
2.6032 
0.919 
  
  
8 
0.017 
0.017 
3.0348 
0.932 
  
  
9 
0.026 
0.026 
4.0376 
0.909 
  
  
10 
0.017 
0.016 
4.4741 
0.923 
  
  
11 
0.065 
0.065 
10.686 
0.470 
  
  
12 
0.011 
0.016 
10.879 
0.539 
  
  
13 
0.015 
0.017 
11.221 
0.592 
  
  
14 
0.012 
0.009 
11.427 
0.652 
  
  
15 
0.004 
0.003 
11.454 
0.720 
  
  
16 
0.013 
0.013 
11.690 
0.765 
  
  
17 
0.032 
0.032 
13.233 
0.720 
  
  
18 
0.003 
0.006 
13.244 
0.777 
  
  
19 
0.005 
0.005 
13.282 
0.824 
  
  
20 
0.008 
0.012 
13.389 
0.860 
  
  
21 
0.022 
0.022 
14.091 
0.866 
  
  
22 
0.012 
0.018 
14.295 
0.891 
  
  
23 
0.018 
0.016 
14.788 
0.902 
  
  
24 
0.018 
0.013 
15.261 
0.913 
  
  
25 
0.003 
0.001 
15.274 
0.935 
  
  
26 
0.004 
0.002 
15.299 
0.952 
  
  
27 
0.006 
0.006 
15.349 
0.964 
  
  
28 
0.003 
0.007 
15.361 
0.974 
  
  
29 
0.014 
0.016 
15.643 
0.979 
  
  
30 
0.005 
0.005 
15.687 
0.985 
  
  
31 
0.015 
0.017 
16.023 
0.988 
  
  
32 
0.027 
0.024 
17.121 
0.985 
  
  
33 
0.013 
0.014 
17.369 
0.988 
  
  
34 
0.007 
0.007 
17.451 
0.992 
  
  
35 
0.004 
0.000 
17.475 
0.994 
  
  
36 
0.000 
0.003 
17.475 
0.996 
Source: Econometric output from Eviews.10 
Autocorrelation 
Partial Correlation 
AC 
PAC 
QStat 
Prob* 

  
  
1 
0.051 
0.051 
3.8894 
0.049 
  
  
2 
0.011 
0.008 
4.0520 
0.132 
  
  
3 
0.017 
0.018 
4.4969 
0.213 
  
  
4 
0.003 
0.001 
4.5104 
0.341 
  
  
5 
0.018 
0.017 
4.9818 
0.418 
  
  
6 
0.007 
0.006 
5.0576 
0.536 
  
  
7 
0.006 
0.005 
5.1161 
0.646 
  
  
8 
0.017 
0.017 
5.5287 
0.700 
  
  
9 
0.027 
0.026 
6.6178 
0.677 
  
  
10 
0.016 
0.014 
7.0002 
0.725 
  
  
11 
0.067 
0.068 
13.533 
0.260 
  
  
12 
0.008 
0.016 
13.639 
0.324 
  
  
13 
0.013 
0.015 
13.895 
0.381 
  
  
14 
0.014 
0.011 
14.185 
0.436 
  
  
15 
0.005 
0.006 
14.225 
0.509 
  
  
16 
0.003 
0.004 
14.242 
0.581 
  
  
17 
0.062 
0.061 
19.983 
0.275 
  
  
18 
0.001 
0.006 
19.986 
0.334 
  
  
19 
0.013 
0.013 
20.248 
0.380 
  
  
20 
0.018 
0.022 
20.716 
0.414 
  
  
21 
0.020 
0.019 
21.315 
0.440 
  
  
22 
0.014 
0.020 
21.601 
0.484 
  
  
23 
0.022 
0.019 
22.354 
0.499 
  
  
24 
0.023 
0.017 
23.133 
0.512 
  
  
25 
0.005 
0.001 
23.172 
0.568 
  
  
26 
0.007 
0.004 
23.240 
0.619 
  
  
27 
0.008 
0.007 
23.344 
0.666 
  
  
28 
0.009 
0.016 
23.460 
0.710 
  
  
29 
0.017 
0.022 
23.902 
0.734 
  
  
30 
0.004 
0.003 
23.930 
0.775 
  
  
31 
0.015 
0.019 
24.279 
0.799 
  
  
32 
0.023 
0.020 
25.089 
0.802 
  
  
33 
0.014 
0.016 
25.403 
0.825 
  
  
34 
0.006 
0.007 
25.460 
0.854 
  
  
35 
0.007 
0.003 
25.540 
0.879 
  
  
36 
0.002 
0.002 
25.545 
0.903 
Source: Econometric output from Eviews.10 
Source: Eviews 10 
Source: Eviews 10 
Source: Eviews 10 
Source: Eviews 10 
Source: Eviews 10 
Source: Eviews 10 
Source: Eviews 10 