Page 140 - Contributed Paper Session (CPS) - Volume 5

CPS1145 Adeniji Oyebimpe Emmanuel et al.
Equation (9) is the log-likelihood lt of Normal, N is the sample sizes of the
series, t is the white noise, zt is sequence of identical independent random
2
variables and t is the conditional variance.
The Log-likelihood for Student-t distribution is

(12)

In the estimation in equation (10) v is the degree of freedom and y (.)
Is the gamma function, for GED it is
(13)

3. Result
To obtain a stationary series, we use the returns Rt =100(log (Yt )-log(Yt-1 ))
where Yt is the closing value of index at month t. The sample statistics for the
returns Rt are exhibited in table 1. For NSE index (sample January 2000 to
September 2018). The time plots which is the first step to examine hidden
characteristic reveals non-stationarity, patterns and clustered volatility.

INDEX MIN MEDIAN MEAN
NSE 1.00 96.50 96.40
MAX SKEWNESS KURTOSIS SHAPIRO-WILK TEST
191.00 -0.00763 -3.2260 0.9538

Descriptive statistics for Returns the skewness is negatively skewed and
also exist negative kurtosis which indicate anomalous distribution. Shapiro-
Wilk test indicate non normality. Out of the 18 models in consideration,
EGARCH-GLBST(1,1) was the best, followed by APARCH-GLBST(1,1) and EGAS
models, in terms of the AIC values (7.856,7.988 and 9.984).The forecast
evaluation criteria (RMSE, AMAPE), EGARCH-GLBST(1,1) model also ranked
best (RMSE =0.281, AMAPE = 0.280), followed by APARCH-GLBST(1,1) model
(RMSE = 0.291, AMAPE = 0.290) and EGAS model (RMSE = 0.309, AMAPE =
0.301). The least performing in terms of forecasts was the GARCH(1,1)-Normal
model.

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