Modelling & Forecasting Volatility of Daily Stock Returns Using GARCH Models: Evidence from Dhaka Stock Exchange

Modelling volatility has become increasingly important in recent times for its diverse implications. The main purpose of this paper is to examine the performance of volatility modelling using different models and their forecasting accuracy for the returns of Dhaka Stock Exchange (DSE) under different error distribution assumptions. Using the daily closing price of DSE from the period 27 January 2013 to 06 November 2017, this analysis has been done using Generalized Autoregressive Conditional Heteroscedastic (GARCH), Asymmetric Power Autoregressive Conditional Heteroscedastic (APARCH), Exponential Generalized Autoregressive Conditional Heteroscedastic (EGARCH), Threshold Generalized Autoregressive Conditional Heteroscedastic (TGARCH) and Integrated Generalized Autoregressive Conditional Heteroscedastic (IGARCH) models under both normal and student’s t error distribution. The study finds that ARMA (1,1)- TGARCH (1,1) is the most appropriate model for in-sample estimation accuracy under student’s t error distribution. The asymmetric effect captured by the parameter of ARMA (1,1) with TGARCH (1,1), APARCH (1,1) and EGARCH (1,1) models shows that negative shocks or bad news create more volatility than positive shocks or good news. The study also provides evidence that student’s t distribution for errors improves forecasting accuracy. With such an error distribution assumption, ARMA (1,1)-IGARCH (1,1) is considered the best for out-of-sample volatility forecasting.


Introduction
Over the past decades, modelling and forecasting volatility of financial time series has become a fertile area for research (Zakaria & Winker, 2012). Many models in the field of academic finance use variance (or standard deviation) as a measure of uncertainty (Niyitegeka & Tewari, 2013). "In most of these models' variance is assumed to be constant through time; this is known as homoscedasticity" (Brooks, 2002, p. 386). Financial time series such as stock prices often exhibit volatility clustering. The time series are found to depend on their own past values and exhibit non-constant variance or heteroscedasticity. A time series with some periods of low volatility and some periods of high volatility is said to be "volatility clustering" (Banumathy & Azhagaiah, 2013). It has been found that the stock market volatility changes with time and exhibits "volatility clustering." The knowledge of volatility is of crucial importance for many economic and financial applications like portfolio management, risk management, asset pricing and investment in general (Floros, 2008;Niyitegeka & Tewari, 2013, Zakaria & Winker, 2012Parvaresh & Bavaghar, 2012). Volatility is the most important variable in evaluating derivative instruments. Volatility is closely related to risk. Investors in the stock market are obviously interested in analysing and learning about the nature of the stock market volatility of stock prices, for high volatility could mean huge losses or gains and hence greater uncertainty (Parvaresh & Bavaghar, 2012).
Several models have been developed since the 1980s that are especially suited to estimate the conditional volatility of financial assets (Zakaria & Winker, 2012). Frequently applied models of this type are the generalized conditional heteroscedastic models (Zakaria & Winker, 2012). Engle (1982) introduced Autoregressive Conditional Heteroscedasticity (ARCH) to the world to model financial time series that exhibit time-varying conditional variance. A generalized ARCH model (GARCH) was extended by Bollerslev (1986). These are popular models for estimating stochastic volatility. These models are widely used in time series econometrics, especially in financial time series analysis. With the introduction of models of ARCH and GARCH, there have been wide empirical applications of modelling volatility of financial time series. However, the GARCH cannot account for leverage and to account for that effect, APARCH, E-GARCH and T-GARCH models have been developed over time.
However, it is widely recognized among researchers that for excess kurtosis along with an increase in data frequency, the rate of return in financial variables might have a levy distribution or a fat-tailed (Mandelbrot, 1963). Under normality assumption for errors, the volatility modelling and forecasting based on such modes will be misleading. The main objective of this paper is to model stock returns volatility in Dhaka Stock Exchange (DSE) by employing different GARCH family type models for daily observations on the index returns series over the period of 27 January 2013 to 06 November 2017. The volatility models employed in this paper include both symmetric and asymmetric GARCH models. Moreover, student's t distribution is used to correctly model and forecast the volatility of stock return and normal distribution for errors is used to compare with student's t distribution for errors. The rest of the paper organized as follows: Section 2 provides the relevant literature review. Section 3 describes data and potential methodology. Section 4 provides estimation results and their discussion respectively. Section 5 provides the results of volatility forecasting both in-sample estimation and out-of-sample forecasting accuracy. Finally, the paper concludes and suggests some policy implications.
In the middle eastern stock markets, EGARCH models are seen to be dominant in determining the leverage effect of daily stock prices (Floros, 2008;Parvaresh & Bavaghar, 2012). Floros (2008) examined the volatility in Egyptian and Israeli stock indices and found coefficients of the EGARCH model showed a negative and significant value for both indices, indicating the existence of the leverage effect. Parvaresh and Bavaghar (2012) have examined GARCH models in forecasting volatility for Tehran Stock Market and the study suggested that GARCH models used in this paper have the same forecasting power while evaluating forecasting with MSE criteria, while CGARCH has the best forecasting power given the log-likelihood is evaluation criteria. Abd El Aal (2011) examined five models for forecasting volatility of the Egyptian stock market index and employed different statistical metrics. After using usual statistical metrics, they found that the EGARCH model beat the other volatility forecasting models for the Egyptian stock market. However, after using DM statistics they found no significant differences between the forecasting volatility models performance.
However, the scholarships relating to African stock markets employed symmetric and asymmetric GARCH models to model volatility that capture the most common stylized facts about index returns such as volatility clustering and leverage effects (Zakaria & Winker, 2002;Niyitegeka & Tewari 2013;Abd El Aal 2011). Zakaria and Winker (2002) examined the return volatility using daily prices of Khartoum Stock Exchange (KSE) and Cairo and Alexandria Stock Exchange (CASE) where the results showed significant evidence for the existence of the leverage effects in the two markets, based on asymmetrical EGARCH (1,1) and TGARCH (1,1) estimation. However, the result of EGARCH and GJR-GARCH (1,1) failed to indicate the existence of leverage effects in South African stock returns (Niyitegeka & Tewari, 2013). In terms of volatility in African stock markets, results indicate the mixed outcome. GARCH-M (1,1) described statistically significant conditional variance for Egyptian and Sudanese stock markets with a positive sign (Zakaria & Winker, 2002). On the other hand, the results from the GARCH (1,1) model show that volatility of stock returns is persistent in South Africa (Niyitegeka & Tewari, 2013). However, some studies are limited as they did not test to what extent volatility forecasts based on the present models are useful in the context of risk management for the stock markets considered (Zakaria & Winker 2002).
Meanwhile, the only western stock markets literature reviewed in this paper, studied two major European stock exchanges using daily data over a 15-years period (Peters, 2001). Study results revealed that overall estimation is improved when fat-tailed densities are considered in the conditional variance and when asymmetric GARCH is used. In addition to that, GJR and APARCH models are found to be giving better forecasts than symmetric GARCH.
South Asian stock markets studied the heteroscedasticity behaviour of the stock markets making use of several GARCH models (Karmakar, 2005;Banumathy & Azhagaiah 2013;Qamruzzaman, 2015). Banumathy and Azhagaiah (2013) showed that bad news or negative shocks create more volatility than positive shocks or good news by giving negative and positive significant coefficients for EGARCH (1,1) and TGARCH (1,1) models respectively. Karmaker (2005) showed the suitability of the GARCH (1,1) model that gave remarkably good forecasts of market volatility. The scholarships again produced mixed results in the South Asian stock market in terms of capturing symmetric and asymmetric volatility. Some studies examined whether there is asymmetric volatility by using the E-GARCH models and observed that volatility is an asymmetric function of past innovation that increases at a higher rate during market decline (Karmakar, 2005). However, GARCH (1,1) and TGARCH (1,1) estimators are found to be the most suitable models to capture the symmetric and asymmetric volatility respectively in some other studies (Banumathy & Azhagaiah, 2013). Qamruzzaman (2015) examined a wide variety of popular volatility models for Chittagong Stock Exchange (CSE) and the results indicated that GARCHz, EGARCH-z, IGARCH-z, GJR-GARCH-z and EGARCH-t are suitable for that specific stock exchange with the volatility of the return being significantly higher after 2009. An important limitation of some studies being their suffering from the constraint of non-calculation of intraday volatility and only used a short period of time-series data (Banumathy & Azhagaiah, 2013).
In a different study, Abdullah, Siddiqua, Siddiquee, and Hossain (2017) tried to model and forecast exchange rate volatility by addressing the issue of error distributional assumption between the Bangladeshi taka and the US dollar. This study attempted to model the dynamics by using five different models from January 1, 2008, to April 30, 2015, under both normal and student's t distribution. The models' findings were compared under the regular normal distribution assumption for the residuals against Student's t-distribution and it was later found that the application of student's t distribution improved forecasting accuracy more than the normal distribution. Moreover, the findings also indicated that for modelling in-sample volatility dynamics, AR (2)-IGARCH (1, 1) was found to be the most accurate, while AR (2)-GARCH (1,1) gave the best performance under error distribution for the outof-sample volatility forecasting.
However, there are relatively fewer studies on the stock return volatility of DSE. In one current example, Huq et al. (2013) modelled the stock return volatility using daily closing price data from December 06, 2010, to March 12, 2013. According to them, ARMA (1,1) with GARCH (1,1) and GARCH (2,1) are more appropriate models for the general index of the Dhaka Stock Exchange (DSE). But this study has some limitations. They addressed the lag specification of the mean equation properly, but they did not consider the excess kurtosis and skewness. Hence, their results may be misleading. Besides, the I-GARCH model was not used even though the sum of the persistence parameter exceeds the unitary value of almost all the papers. We were appreciative of the work of Abdullah et al. (2017) on exchange rate volatility and therefore attempted to apply the I-GARCH model in the field of stock return volatility of DSE. However, there is a need to identify the true nature of stock market volatility in an emerging market like Bangladesh. Moreover, selecting proper mean equations, addressing excess kurtosis by using student's t distribution and selecting appropriate models may contribute to the field of stock return volatility of DSE. This paper, therefore, analyses the presence and pattern of the volatility clustering in the Dhaka stock index return series using the GARCH family of models. Additionally, the study examines the presence of leverage effect or asymmetric information effect in the DSE index and thus contributes to the existing literature.

Data Sources and Variable Formation
The study is based on the secondary data that was collected from Dhaka Stock Exchange Indices. The daily closing price of the DSE general index namely DSEX over five years from 27 January 2013 to 06 November 2017 were considered for the analysis. The study used 1153 daily observations excluding holidays. Since the daily closing price is normally nonstationary, it is inappropriate for the analysis. However, several studies (Karmakar 2005, Abdullah et al., 2017 suggest estimating the volatility of the return series. The DSE daily stock return series is, therefore, calculated using the following log transformation: Where + is the logarithmic return on DSE indices for time t, + is the closing price at time t, and +() is the corresponding price in the period at time t-1. The statistical software EViews 7 was used for the quantitative analysis.

Unit Root Test
In a time series, the stationary check is a must. Unit root test is usually used to test whether the data are stationarity. In this regard, the study performed Augmented Dickey-Fuller Test (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) Test.

The ARCH Model
It is well known that volatility is commonly modelled by GARCH family models. Usually, one can use the mean equation for the level of the series and then the ARCH model is used for modelling the variance. When data are serially correlated, the misspecification of the mean equation could fail to address the autocorrelation problem that could arise in the volatility model. Hence, the accurate specification of the mean equation is very important. We, therefore, estimated all the GARCH family models for the following appropriate mean equation: We used five different GARCH family models to specify the variance equation to model volatility for different purposes. The sensitivity of the estimation results of the models was checked by changing distributional assumptions. The distributional assumption is changed from normal to student's t distribution. The reason is that in many pieces of literature on financial asset returns, it is established that the return variable is more likely to follow a "levy distribution" with "fat tails" and kurtosis is likely to increase with data frequency (Andersen & Bollerslev, 1998). The useful variance equation is assumed as: Variance equation:

The Generalized ARCH (GARCH) Model
The Pioneer of modelling volatility, Engle (1982) used Autoregressive Conditional Heteroscedasticity (ARCH) model to model volatility. But the main problem with the ARCH model is that in practice, a long lag is often required to capture the time-varying volatility. The GARCH model proposed by Bollerslev (1986) allows conditional variance to depend upon its lag which typically reduces the number of ARCH lags required. So, the conditional variance equation should follow as: GARCH (1,1): ℎ + = 9 + +() . + βℎ +() Here, the GARCH (1,1) model has one ARCH term denoted as +() . and one GARCH term denoted as ℎ +() . For the variance to remain well behaved (finite and positive), some restrictions are needed: α ≥ 0, 9 >0, ≥ 0. The sum of the ARCH and GARCH coefficients leads to the persistency of volatility shocks. To ensure that series ε " is stationary and the variance is well behaved, it is necessary to assume that α +β˂1.
3.2.4 The Symmetric Power ARCH or (APARCH) model Ding, Granger, and Engle (1993) introduced the asymmetric power ARCH or (APARCH) model. The APARCH (1,1) can be expressed as: This model is developed to allow for possible non-linearity in the parameters of the variance equation. Here ɗ donates the power parameter that requires that ɗ>0 and γ is the parameter capturing any asymmetric or leverage effect which requires the condition |γ|<1.

The Exponential GARCH (EGARCH) model
The main drawback of the standard GARCH (1,1) model is that the conditional variance is unable to respond asymmetrically to the rise and fall in the stock returns. This model suggests that the shock in +() has the same effect irrespectively of whether +() > 0 or +() < 0. A typical feature of financial data is that negative shocks or bad news create more volatility than positive shocks or good news. To test the presence of leverage effect in financial data, Nelson (1991)  Where α is the size parameter measuring the magnitude of shocks, γ is the asymmetric parameter measuring leverage effect, β measures the persistence in conditional volatility irrespectively of shocks to the market. An important feature of the EGARCH model is that there is no need for any non-negativity restrictions.

The Integrated GARCH (IGARCH) Model
GARCH model with unit root (non-stationary GARCH model) can be regarded as an integrated GARCH or IGARCH model. This model was originally developed by Engel (1982) and Bollerslev (1986). In practice, when the parameters of the GARCH model are restricted to a sum equal to one and ignore the constant term, a standard GARCH model is transformed into an IGARCH model.

Results and Discussion
The daily closing price of the DSE index is non-stationary. This non-stationary behaviour can be seen from the graph of the daily price which is presented in Figure 1 (Appendix). To make the series stationary, the daily closing price of the DSE index is converted into daily logarithmic return series. This return series is now stationary, which is shown in Figure 2. (Appendix). Descriptive statistics on DSE stock return are summarized in Table 1. The mean of the returns is positive, indicating that the price has increased over the period. Statistically, the risk or volatility is the dispersion of the returns. Daily performance (average probability) for the period is 0.000355 and the risk (standard deviation) per day is 0.008394 which reflects the high volatility of the Dhaka Stock Index. The descriptive statistics show that the returns are negatively skewed, indicating that there is a high probability of earning returns that is greater than the mean. The kurtosis of the series is greater than 3 which implies that the return series is fat-tailed and does not follow a normal distribution. The histogram of the return series shown in Figure 3 (Appendix) remains centred at the zero with a slight negative bias (-0.161429) and a kurtosis value of (6.588151) which shows excess kurtosis regarding the standard normal and is further confirmed by the Jarque-Bera test statistics which is significant of 1% level and hence the null hypothesis of normality is rejected.
To detect if the DSE return series is stationary, a unit root test is carried out with the statistical Augmented Dickey-Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test.  Table 2 shows the presence of unit root in the series tested using ADF and KPSS tests. The p -values of ADF with both "intercept" & "trend and intercept" are less than 0.01 which leads to conclude that the data of the time series for the entire period is stationary. The p-value of the KPSS test with both "intercept" & "trend and intercept" is greater than 0.01 which leads us to conclude that the null hypothesis of "return series is stationary" is accepted at a 1% level. Both the ADF and KPSS test reported in Table 2 confirms that the return series is stationary. 0.0000 Standard Errors are in parenthesis. ***,**,* indicates significant at 1%, 5% and 10% level respectively.
The estimation result of the conditional mean model for the logarithmic stock return using the Ordinary Least Squares (OLS) method is presented in Table 3. Since the series was observed to be mean reverting, OLS was applied to estimate the regression. The model was not augmented with further AR and MA terms because they were not significant.
The Heteroscedasticity test is applied to find out the presence of ARCH effect in the residuals of the return series. From Table 3, it is concluded that the F-statistics is highly significant. Since the p-value is less than 0.01, the null hypothesis of "no ARCH effect" is rejected at a 1% level which confirms the presence of ARCH effects in the residuals of time series models in the returns.
The volatility clustering of return series for the study period from 27 January 2013 to 06 November 2017 is also been observed (Figure 4 (Appendix)). It shows that the period of low volatility tends to be followed by a period of low volatility for a prolonged period and the period of high volatility is followed by a period of high volatility for a prolonged period, which means the volatility is clustering and the return series vary around the constant mean, but the variance is changing with time. Hence, these results suggest the estimation of GARCH family models.
Since the ARCH effect is detected in the model, GARCH family model is therefore used for modelling the volatility of return series in the Dhaka Stock Exchange Market.  (1) 0.0540 0.0585 Standard Errors are in parenthesis. ***,**,* indicates significant at 1%, 5% and 10% level respectively.
The GARCH (1,1), model is applied for the purpose of capturing variance dynamics. Table 4 shows the estimation results. Here, it is evident that the autoregressive coefficients of this lagged dependent variable for the mean equation ƿ ) and MA (1) coefficient ƿ . for the mean equation are statistically significant at 1% level.
The coefficients of the GARCH components (α and β) are positive and statistically significant at a 1% level (Table  4). In the conditional variance equation, the estimated β coefficient shows that the volatility is persistent. The sum of these parameters (α and β) is 0.99745, which is close to unity indicating that the stock will persist to many future periods. Further, ARCH-LM test is employed to check ARCH effect in residuals and from the result, it is inferred that the p>0.05, which led to conclude that the null hypothesis of "no ARCH effect" is accepted. In other words, the test statistics do not support any additional ARCH effect remaining in the residuals of the models, which implies that the variance equation is well specified for the market.  (1) 0.0430 0.0425 Standard Errors are in parenthesis. ***,**,* indicates significant at 1%, 5% and 10% level respectively.
The results from the APARCH model is presented in Table 5, and it is evident that the autoregressive coefficient of the lagged dependent variable ) for the mean equation and MA (1) coefficient . are statistically significant at the 1% level. The coefficients α and β are again found to be positive and statistically significant at 1% level, having a sum greater than 1 for both distributions. The coefficient ɗ is positive and significant and not equal to 2 which implies that it is not a standard GARCH model (Ding et al., 1993). The significance and sign of the coefficient γ determine the leverage effect.
The positive significant value of γ indicates the existence of a leverage effect where negative past values of + increase volatility more than positive past values of the same magnitude. Table 5 also shows, the leverage effect is positive and significant. Thus, an asymmetric volatility effect exists for stock returns. The coefficients of the ARCH & GARCH sum to more than 1 and the constant term in the variance equation of the APARCH model using both normal and student t distribution are not statistically different from 0. Thus, as the necessary nonnegativity restrictions have not been satisfied, so the variance equation is not well behaved.
To capture the asymmetric effect in the return series and eliminate the problem of non-negativity restrictions, we estimate an EGARCH model. Table 6 shows the estimation result of the EGARCH (1,1) model using both normal and student t distribution.    (1) 0.0765 0.0739 Standard Errors are in parenthesis. ***,**,* indicates significant at 1%, 5% and 10% level respectively.
The sum of ARCH(α) & GARCH (β) is greater than one (Table 6), reporting that the conditional variance is explosive. Here in the variance equation γ is popularly known as the "asymmetry parameter" and a represents the "size parameter". The estimated coefficients are statistically significant at a 1% level. The leverage coefficient, γ is negative and statistically significant at 1% level, exhibiting the leverage effect in return during the study period. The analysis reveals that there is a negative correlation between past return and future return. Hence, EGARCH (1,1) model supports the presence of leverage effect on the DSE return series. Finally, the ARCH-LM test statistics reveals that the null hypothesis of no heteroscedasticity in the residuals is accepted.
An alternative model to test for asymmetric volatility in the DSE return is TGARCH. Table 7 shows the estimation results of TGARCH using both normal and student's t distribution.  (1) 0.1072 0.1065 Standard Errors are in parenthesis. ***,**,* indicates significant at 1%, 5% and 10% level respectively. Table 7 shows that the coefficient of leverage effect is positive and significant at a 1% level, which implies that a negative shock or bad news has greater volatility on the condition variance than the positive shocks or good news. The diagnostic test is performed to test whether there is an ARCH effect. The ARCH-LM test statistics for TARCH (1,1) model show that there are no additional ARCH effects in the residuals of the model.
Since it has been found that the sum of the persistence parameters exceeds 1 for some models, it can be deduced that the variance might not be well behaved in such models. Therefore, it would be interesting to model volatility clustering with such models while imposing restrictions on the persistence parameters. Our popular restriction on the "persistent parameters sum up to unit". Thus, the estimation of GARCH models with this restriction leads to the IGARCH model. Table 8 shows the estimation result of IGARCH (1,1) using both normal and student t distribution.  (1) 0.1360 0.1492 Standard Errors are in parenthesis. ***,**,* indicates significant at 1%, 5% and 10% level respectively.
The IGARCH (1,1) model successfully overcomes all of the diagnostic tests for both normal and student's t distribution, is used as the error distribution (Table 8). There is no additional ARCH effect and no autocorrelation detected in the regular and squared residuals. Finally, the evidence indicates that all of the models (GARCH, EGARCH, TGARCH & IGARCH without APARCH) satisfy the required diagnostic standard under both normal distributions as well as student's t distribution as the assumption for the residuals.

In-sample estimation performance
To find out whether the accuracy of volatility forecasting among the five models (GARCH, APARCH, EGARCH, TGARCH & IGARCH) varied with distributional assumptions, we compared the log-likelihood, Schwarz Bayesian Information Criterion (BIC), and Akaike Information Criterion (AIC) for all those models, estimating for the whole sample observations under normal and student's t distribution. Table 9 shows the results. The performance of each model improved under the student's t distribution. The reason behind that log-likelihood increased while both AIC and BIC decreased compared to the normal distributional assumptions applied for the residuals. Considering the student's t distribution for the residuals, a comparison of log-likelihood indicates that among all the models used for in-sample estimation, ARMA (1,1)-APARCH (1,1) is the best since it has maximum likelihood and a comparison of BIC and AIC indicators that among all the models used for in-sample estimation, ARMA (1,1)-TGARCH (1,1) is the best since it has lowered BIC and AIC. However, the ARMA (1,1)-APARCH (1,1) model is more problematic since it can't overcome any of the diagnostic tests, that is, there exist additional ARCH effects and autocorrelation problem in the residuals. Without APARCH (1,1), the other models successfully overcome all the diagnostic tests. Without APARCH (1,1), a comparison of all 3 indicators indicates that ARMA (1,1)-TGARCH (1,1) is the best since it has maximum likelihood and minimum BIC and AIC.

Out of sample forecasting performance
The accuracy of a forecasting model is its out-of-sample performance, which measures its performance in "realtime." Out-of-sample forecasting is a stepwise method for stimulating real-time performance. To find the out-ofsample forecasting accuracy of the models, we created a pseudo sample using the period from January 27  For the ARMA (1,1)-EGARCH (1,1) model, RMSE, MAE, and TI decreased while MAPE increased when changing distribution assumption. Thus, this model's forecasting accuracy was improved under the student's t distribution. For ARMA (1,1)-TGARCH (1,1) model which had the best in-sample estimation accuracy under student's t distribution showed lower accuracy when such distribution was used for out of sample forecasting since two of the four indicators increased, one (RMSE) constant and another TI decreased. Without ARMA (1,1)-TGARCH (1,1) model, the rest of the model's forecasting accuracy was improved under the student's t distribution assumption. Considering the student's t distribution for residuals, a comparison of RMSE, MAE, MAPE, and TI indicate that ARMA (1,1)-IGARCH (1,1) is the best for out-of-sample forecasting.

Conclusion
It is well known that the capital market is the engine of growth for an economy since it contributes to a country's economic growth through the creation of wealth. Since the stock market attracts investment, stock return volatility will have a significant effect on investment and consequently on the whole economy. For this reason, it is very important to properly model and forecast stock return volatility. In this study, the volatility of the Dhaka Stock Exchange (DSE) return is tested using the symmetric and asymmetric GARCH models. The Dhaka Stock Exchange (DSE) is the country's leading stock exchange. The daily closing prices of DSE for five years are collected and modelled using five different GARCH models that capture the volatility clustering and leverage effect for the study period i.e., from 27 January 2013 to 06 November 2017. To estimate volatility models, the leptokurtic fat-tailed nature of the stock return series usually provides a reason for using skewed distribution such as student's t distribution. The main objective was on whether the same result exists in the stock return and whether the results were improved with student's t distribution. In particular, the volatility dynamics of the daily stock return of DSE are modelled using GARCH models such as GARCH, APARCH, EGARCH, TGARCH, and IGARCH. The findings from the models under the normal distribution assumption for residuals were compared to the student's t distribution. All models successfully passed the diagnostic tests under both distribution assumptions for residuals only except APARCH (1,1) model.
In the sample, estimation accuracy was improved when the student's t distribution was used. For modelling insample volatility dynamics, ARMA (1,1)-T-GARCH (1,1) was found to be the most accurate model. We further tried to find the appropriate model for out-of-sample forecasting. In the case of out-of-sample forecasting accuracy, ARMA (1,1)-I-GARCH (1,1) is considered the best compared to the other three models since MRSE, MAE, and TI were lower than the other models under student's t distribution. Since an investor is always interested in making easy and riskless money, he or she should take into consideration all other factors before investing in the stock market. Therefore, valuations in such markets should be dealt with carefully by considering conditional variance. The limitation of the study is that the study used only 5 years' data of DSE. Future researchers might study to what extent volatility forecasts based on the present models are useful in the context of structural break, the causes of it and how it can be considered in the volatility equations.