**3.1 Descriptive statistics**

The statistical distributions of the 252 monthly observations of stock price and oil price with their returns used in this study are presented in **Table 1**. The average monthly observation of the oil price returns is �0.0013%, which implies that there were losses and low returns on oil revenue during the period of study. The high difference between the maximum oil price of \$US132.72 and the minimum value of \$US18.38 confirms the high volatile nature of the oil price. For the stock price returns, the minimum value is negative with a value of �0.3659. This implies that the stock price returns is less volatile than the oil price returns with minimum value of �0.55%. Although, there is also a large difference between the maximum value of the stock price with N65652.38 in billion and the minimum values of N5892.8 billion. The variability is just lower compared to that of the oil price. The standard deviation, skewness and kurtosis greater than zero imply that distribution is not normally distributed except for both returns that are close to zero and being normal. The positive skewness of 0.39% and 0.55% for oil price and stock price imply that their distributions are skewed to the right. On the other hand, the negative skewness of �1.75% and �0.47% for oil price returns and stock price returns imply that their distributions are skewed to the left. Furthermore, the kurtosis of oil price with value of 2.09% and the stock price with value 3.51 imply normal distribution because the values are less than 3. However for the returns, the kurtosis value of 9.08 and 7.71% for both oil price returns and stock price returns denote leptokurtic characteristic. Lastly, the null hypothesis for Jarque-Bera is that the data is normally distributed, however, with the probability value of 0.00 less than 0.05% in **Table 1**, then the null hypothesis is rejected and the alternative hypothesis that the data are

not normally distributed is accepted. It is evident that the statistical properties of the variables used in this study can be described as fat tailed, leptokurtic and deviated from normal distribution which is typical of financial time series, risks and

**Variables Levels Status Variables Levels Status** Oil price returns 10.0663 I(0) Oil price returns 10.015 I(0) Stock price returns 13.5579 I(0) Stock price returns 13.5579 I(0)

*Volatility Effects of the Global Oil Price on Stock Price in Nigeria: Evidence from Linear…*

F-Statistics 7.9138 Prob. F(1,241) 0.00 Obs\*R-squared 7.7257 Prob. Chi-Square(1) 0.00 Scale explained SS 5854 Prob. Chi-Square(1) 0.00

**Augmented Dickey Fuller test Phillips-Perron test**

*DOI: http://dx.doi.org/10.5772/intechopen.93497*

*The critical values are 3.4573, 2.8733 and 2.5731 for 1, 5, and 10%, respectively.*

The first exercise after the descriptive analysis is to verify the stationary properties of the variables used in the analysis and then test for the ARCH effect on the variables. Once the variables are stationary and ARCH effect is present, then we can proceed to estimate the GARCH models. The Augmented Dickey Fuller [22] and the Philips-Perron [23] tests were conducted and the results shown in **Table 2**. The unit root results show that both oil price returns and stock price returns are stationary at

levels. The stationarity of the returns of the variable of interest is one of the

The final preliminary test is to test for ARCH effects using Breusch-Pagan-Godfrey method of Engle [24] to verify the presence of heteroscedasticity and proceed to the GARCH process. The heteroscedasticity test presented in **Table 3** shows the presence of heteroscedasticity, which means that the variance is not constant over time (see also Appendix 5 for additional evidence of heteroscedasticity with the fat tail of the histogram distribution). The null hypothesis is that there is no presence of heteroscedasticity in the returns series. And since the probability value is less than 0.05%, then the null hypothesis is rejected and the alternative hypothesis of presence of ARCH effects or heteroscedasticity is accepted.

The presence of the ARCH effects in our variables as presented in **Table 3** endorses the use of the GARCH models. There are many types of GARCH models. We have the symmetric (linear) GARCH, which is the normal GARCH and asymmetric (nonlinear) GARCH such as exponential GARCH (EGARCH) and the Threshold GARCH (TGARCH) or Glosten, Jagannathan and Runkle GARCH

conditions for carrying out the GARCH process.

**4. The linear and non-linear GARCH models**

returns.

**Table 3.**

**Table 2.**

*Results of the unit root tests.*

*Breusch-pagan-Godfrey test.*

**3.2 Preliminary test**

(GJR-GARCH).

**175**


**Table 1.** *Descriptive analysis.* *Volatility Effects of the Global Oil Price on Stock Price in Nigeria: Evidence from Linear… DOI: http://dx.doi.org/10.5772/intechopen.93497*

