**2. Empirical literature reviews of previous studies**

Emenogu, et al. [3] modeled and forecasted the Guaranty Trust (GT) Bank daily stock returns from January 22,001 to May 82,017 data set collected from a secondary source. The ARMA-GARCH models, persistence, half-life and backtesting were used to analyzed the collected data using student t and skewed student tdistributions, and the analyses are carried out R environment using rugarch and performanceAnaytics Packages. The study revealed that using the lowest information criteria values only could be misleading rather we added the use of backtesing. The ARMA(1,1)-GARCH(1,1) models fitted exhibited high persistency in the daily stock returns while the days it takes for mean-reverting of the models is about 5 days, but unfortunately the models failed backtesting. The results further revealed ARMA(1,1)-eGARCH (2,2) model with student t distribution provides a suitable model for evaluating the GT bank stock returns among the competing models while it takes less than 30 days for the persistence volatility to return back to its average value of the stock returns. They recommended that researchers should adopt backtesting approach while fitting GARCH models while GT bank stocks investor should be assured that no matter the fluctuations in the stock market, the GT bank stock returns has the ability to returns to its mean price return.

Asemota and Ekejiuba [6] examined the volatility of banks equity weekly returns for six banks (coded B1 to B6) using GARCH models. Results reveal the presence of ARCH effect in B2 and B3 equity returns. In addition, the estimated models could not find evidence of leverage effect. On evaluating the estimated models using standard criteria, EGARCH (1, 1) and CGARCH (1, 1) model in Student's t-distribution are adjudged the best volatility models for B2 and B3 respectively. The study recommends that in modeling stock market volatility, variants of GARCH models and alternative error distribution should be considered for robustness of results. The study also recommended for adequate regulatory effort by the CBN over commercial banks operations that will enhance efficiency of their stocks performance and reduce volatility aimed at boosting investors' confidence in the banking sector.

forecasting financial time series [2], this is because the ARMA and ARIMA models are used to model conditional expectation of a process but in ARMA model, the conditional variance is constant. This means that ARMA model cannot capture process with time-varying conditional variance (volatility) which is mostly

In economic and financial time series literatures, time-varying is more common than constant volatility, and accurate modeling of time volatility is of great importance in financial time series analysis by financial econometricians [4]. In practice, financial time series contains uncertainty, volatility, excess kurtosis, high standard deviation, high skewness and sometimes non normality [3]. Therefore, to model and capture properly the characteristics of financial time series models such as Auto-Regressive Conditional Heteroscedastic (ARCH), Generalized Auto-

Regressive Conditional Heteroscedastic (GARCH), multivariate GARCH, Stochastic volatitlity (SV) and various variants of the models have been proposed to handle these characteristics of financial time series [5]. This chapter would focus on univariate GARCH models. In practice, the backtesting approach compliment the estimated GARCH model, in order to select a reliable GARCH model useful for real

This book chapter aimed at obtaining reliable GARCH model via backtesting

Emenogu, et al. [3] modeled and forecasted the Guaranty Trust (GT) Bank daily stock returns from January 22,001 to May 82,017 data set collected from a secondary source. The ARMA-GARCH models, persistence, half-life and backtesting were

used to analyzed the collected data using student t and skewed student tdistributions, and the analyses are carried out R environment using rugarch and performanceAnaytics Packages. The study revealed that using the lowest information criteria values only could be misleading rather we added the use of backtesing. The ARMA(1,1)-GARCH(1,1) models fitted exhibited high persistency in the daily stock returns while the days it takes for mean-reverting of the models is about 5 days, but unfortunately the models failed backtesting. The results further revealed ARMA(1,1)-eGARCH (2,2) model with student t distribution provides a suitable model for evaluating the GT bank stock returns among the competing models while it takes less than 30 days for the persistence volatility to return back to its average value of the stock returns. They recommended that researchers should adopt backtesting approach while fitting GARCH models while GT bank stocks investor should be assured that no matter the fluctuations in the stock market, the GT bank

stock returns has the ability to returns to its mean price return.

Asemota and Ekejiuba [6] examined the volatility of banks equity weekly returns for six banks (coded B1 to B6) using GARCH models. Results reveal the presence of ARCH effect in B2 and B3 equity returns. In addition, the estimated models could not find evidence of leverage effect. On evaluating the estimated models using standard criteria, EGARCH (1, 1) and CGARCH (1, 1) model in Student's t-distribution are adjudged the best volatility models for B2 and B3 respectively. The study recommends that in modeling stock market volatility, variants of GARCH models and alternative error distribution should be considered for robustness of results. The study also recommended for adequate regulatory effort by the CBN over commercial banks operations that will enhance efficiency of their stocks performance and reduce volatility aimed at boosting investors' confidence in

common with economic and financial time series data [3].

*Linked Open Data - Applications,Trends and Future Developments*

approach using daily Zenith bank Nigeria plc stock returns.

**2. Empirical literature reviews of previous studies**

life application.

the banking sector.

**100**

Adigwe, et al. [7], examined the effect of stock market development on Nigeria's economic growth. The objective of the study was to determine if stock market development significantly impact on the country's economic growth. Secondary data were employed for the study covering 1985 to 2014. Ordinary Least Square (OLS) econometric technique was used for the time series analysis in which variations in economic growth was regressed on market capitalisation ratio to GDP, value of stock traded ratio to GDP, trade openness and inflation rate. The analysis revealed that stock market has the potentials of growth inducing, but has not contributed meaningfully to Nigerian economic growth, since only 26.5% of variations in economic growth were explained by the stock market development variables. Based on this, they suggested for an encouragement of more investors in the market, improvement in the settlement system and ensuring investors' confidence in the market.

Yaya, et al. [8] examined the application of nonlinear Smooth Transition- Generalized Autoregressive Conditional Heteroscedasticity (ST-GARCH) model of Hagerud on prices of banks'shares in Nigeria. The methodology was informed by the failure of the conventional GARCH model to capture the asymmetric properties of the banks' daily share prices. The asymmetry and non-linearity in the model dynamics make it useful for generating nonlinear conditional variance series. From the empirical analysis, we obtained the conditional volatility of each bank's share price return. The highest volatility persistence was observed in Bank 6, while Bank 12 had the least volatility. Evidently, about 25% of the investigated banks exhibited linear volatility behavior, while the remaining banks showed nonlinear volatility specifications. Given the level of risk associated with investment in stocks, investors and financial analysts could consider volatility modeling of bank share prices with variants of the ST-GARCH models. The impact of news is an important feature that relevant agencies could study so as to be guided while addressing underlying issues in the banking system.

Emenike and Aleke [9] studied the daily closing prices of the Nigerian stocks from January 1996 to December 2011 used the asymmetric GARCH variants. Their result showed strong evidence of asymmetric effects in the stock returns and therefore proposed EGARCH as performing better than other asymmetric rivals.

Arowolo [10] examined the forecasting properties of linear GARCH model for daily closing stocks prices of Zenith bank Plc in the Nigerian Stock Exchange. The Akaike and Bayesian Information Criteria (AIC and BIC) techniques were used to obtain the order of the GARCH (p,q) that best fit the Zenith Bank return series. The information criteria identified GARCH (1,2) as the appropriate model. His result further supported the claim that financial data are leptokurtic.

Emenike and Ani [11], examined the nature of volatility of stock returns in the Nigerian banking sector using GARCH models. Individual bank indices and the Allshare Index of the Nigerian Stock Exchange were evaluated for evidence of volatility persistence, volatility asymmetry and fat tails using data from 3 January 2006 to 31 December 2012. Results obtained from GARCH models suggest that stock returns volatility of the Nigerian banking sector move in cluster and that volatility persistence is high for the sample period. The results also indicate that stock returns distribution of the banking sector is leptokurtic and that sign of the innovations have insignificant influence on the volatility of stock returns of the banks. Finally, the findings of this study show that the degree of volatility persistence is higher for the All Share Index than for most of the banks.

Abubakar and Gani [12] re-examined the long run relationship between financial development indicators and economic growth in Nigeria over the period 1970–2010. The study employed the Johansen and Juselius (1990) approach to cointegration and Vector Error Correction Modeling (VECM). Their findings

revealed that in the long-run, liquid liabilities of commercial banks and trade openness exert significant positive influence on economic growth, conversely, credit to the private sector, interest rate spread and government expenditure exert significant negative influence. The findings implied that, credit to the private sector is marred by the identified problems and government borrowing and high interest rate are crowding out investment and growth. The policy implications are financial reforms in Nigeria should focus more on deepening the sector in terms of financial instruments so that firms can have alternatives to banks' credit which proved to be inefficient and detrimental to growth, moreover, government should inculcate fiscal discipline.
