Page 135 - Contributed Paper Session (CPS) - Volume 5

CPS1145 Adeniji Oyebimpe Emmanuel et al.

On jumps models and newly asymmetric
innovations in volatility models and applications
2
1,2
1
Adeniji Oyebimpe , Shittu Olarenwaju , Yaya Olarenwaju
1 Independent National Electoral Commission (INEC), Nigeria and University of Ibadan
2 University of Ibadan, Nigeria

Abstract
Generalised Autoregressive Conditional Heteroskedasticity (GARCH) models
have been used to model non-constant variances in financial time series
models. Previous works have assumed error innovations of GARCH models of
order (p,q) as: Normal, Student-t and Generalised Error Distribution (GED), but
these distributions failed to capture conditional volatility series adequately,
leading to low forecast performance. This study is therefore aimed at
developing variants of GARCH(p,q), Asymmetric Power ARCH (APARCH(p,q))
models, Exponential GARCH EGARCH(p,q) model and comparison with Jumps
GARCH models such as Generalized Autoregressive Score (GAS) , the
Exponential GAS (EGAS) and the Asymmetric Exponential GAS (AEGAS)) with
asymmetric error innovations for improved forecast estimates. The two error
innovations considered were the Generalised Length Biased Scaled-t (GLBST)
and Generalised Beta Skewed-t (GBST) distributions, obtained by remodifying
Fisher Concept of Weighted Distribution and McDonald Generalised Beta
Function, respectively, in the Student-t distribution. The properties of the
proposed distributions were investigated. The proposed innovations were
imposed on GARCH(1,1), EGARCH(1,1) APARCH(1,1) models to obtain GARCH-
GLBST(1,1) and APARCH-GLBST(1,1), EGARCH-GLBST(1,1) models,
respectively. Similarly, GARCH-GBST(1,1), EGARCH -GBST(1,1), APARCH-
GBST(1,1) models were also obtained by incorporating proposed innovations
into GARCH(1,1), EGARCH(1,1) APARCH(1,1) models. Data from the Central
Bank of Nigeria All Share Index (ASL) were used to illustrate the models. The
proposed models were compared with jumps and classical models. The
performance of the proposed models over the existing ones were investigated
using the Log-likelihood function, Root Mean Square Error (RMSE), Adjusted
Mean Absolute Percentage Error (AMAPE) and Akaike Information Criterion
(AIC). 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. The proposed volatility
models with error innovations outperformed existing models in terms of
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