Global Journal of Human Social Science, E: Economics, Volume 23 Issue 2

where ℎ is the conditional variance, t denotes time, and is the lagged squared error term. Themodel spefies that the conditional variance at time t depends on both the past values of the shocks captured by lagged squared error terms and past figures of itself. The GARCH ( p,q ): ℎ model whengeneralized becomes; where P =0, equation (6) reduces to ARCH( q ). Drawing insights from GARCH and threshold GARCH, Nelson (1995) introduced exponential GARCH to capture the test for asymmetries. When bad news filter into the market, assets tend toenter into a state of turbulence and volatility increases. Unlike the case of the TGARCH, the EGARCH uses the log of the series as the dependent variable and not the levels. The conditional variance for the EGARCH (p,q) model is given as; Where log( ℎ ) denotes the log of the variance series, which makes the leverage effect exponential instead of quadratic. The implication is that the estimates are non-negative. V denotes theconstant, represents the ARCH effects, denotes the asymmetric effect, and represents the GARCH effect. The condition is that if 1 = 2 = ⋯ = 0, the model is symmetric. However, where < 0, it implies that negative shocks generate larger volatility than good news. d) Diagnostics test for the EGARCH The preferred model must have the following features; the model must be parsimonious; the ARCH and GARCH coefficients must be statistically significant; the adjusted R-square and the log-likelihood ratio must be high; the SIC information criterion which gives the heaviest penalties for loss of degrees of freedom must be low; and must pass both heteroscedasticity and autocorrelation test. Every model may not pass all these specifications but there could be a reasonable tradeoff. In GARCH diagnostics, a normality test is not necessary because, by nature,the GARCH model have fat tails and are either skewed to the left or right. IV. R esults and D iscussions The plot of the GSECI for the period under study is shown in figure 1. The series is observed to be declining sharply from the last quarter of 2018 and continues to depict a slow downward trend till quarter four of 2019 where it gained some momentum increased slightly. At the beginning of 2020, the GSECI showed a downward trend from quarter one to quarter three. © 2023 Global Journals Volume XXIII Issue II Version I 54 Global Journal of Human Social Science - Year 2023 ( )E Impact of COVID-19 on Stock Market Volatility and Forecast using ARIMA and EGARCH GARCH( p,q ): ℎ = +∑ ℎ − + ∑ − 2 −1 2 (6) log(ℎ ) = + ∑ | − √ℎ − | + =1 ∑ | − √ℎ − | + ∑ log(ℎ − ) =1 =1 (7) 1,800 2,000 2,200 2,400 2,600 2,800 3,000 3,200 IV I II III IV I II III 2018 2019 2020 Stock Exchange Composite Index