Page 422 - Contributed Paper Session (CPS) - Volume 4

CPS2509 D.L Sepato et al.

Modelling volatility with outlier detection in
asymmetric GARCH (p, q) models on JSE index
2
1
2
D.L Sepato , N.D Moroke , J.T Tsoku
1 Nelson Mandela University
2 North West University

Abstract
Financial data often contain observations caused by unexpected events, called
interventions, and such extreme returns are often found to disturb volatility
less than a standard time series model would forecast. The main purpose of
this study is to assess the performance of GARCH type family models with
outlier(s) from a set of data. An iterative procedure is given for the outlier’s
detection and correction method to check the presence of any type of the four
common outliers in financial data. The study explored through the guidance
of the ACFs and PACFs the ARMA enhanced GARCH models such as the ARMA
(0, 2)-GARCH (1, 1), ARMA (0, 2)-EGARCH (1, 1) and ARMA (0, 2)-GJR-GARCH
(1, 1) models to assess the volatility in stock returns data. The study used daily
time series data from the year 03 January 2011 until 21 April 2016 was sourced
from the JSE database. ARMA (0, 2)-EGARCH (1, 1) model was confirmed to be
adequate and was appropriate after the outliers were removed. The model was
recommended for further analyses and were later used for producing forecasts
of JSE stock returns.

Keywords
ARCH; GARCH-variants; Additive outlier; Level shift outlier; Temporary change
outlier; Innovation outlier; JSE index

1. Introduction
Modelling volatility of financial time series is a key area of investigation in
econometrics. Though there are many customary volatility Generalised
Autoregressive Conditional Heteroscedastic (GARCH) models being used, to
capture the stylised facts of financial time series, a drawback of the model is
that it cannot capture the asymmetric features found in financial returns, thus,
to bridge the gap various asymmetric GARCH models have been proposed
(Raziq, Iqbal and Talpur, 2017).
There is a dearth of literature on studies that detect outliers in time series
prior to modelling and producing forecasts. The main objective of this study
was to assess of the performance the asymmetric GARCH-type models in
outlier free data. Therefore, outliers may also introduce bias in the estimated
parameters of GARCH models.

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