Page 136 - Contributed Paper Session (CPS) - Volume 5

CPS1145 Adeniji Oyebimpe Emmanuel et al.
fitness of conditional volatility and forecasts. The proposed models will be
good alternatives for volatility modelling of symmetric and asymmetric stock
returns.

Keywords
GARCH models; Generalised beta skewed–t distribution; Generalised length
biased Scaled distribution; Root mean square error; Jumps Models

1. Introduction
Volatility models are dynamic models that address unequal variances in
financial time series, the first and formal volatility model is the Autoregressive
Conditional Heteroskedasticity (ARCH) model by Engle Robert (1982). The
history of ARCH is a very short one but its literature has grown in a spectacular
fashion. Engle's Original ARCH model and it various generalization have been
applied to numerous economic and financial data series of many countries.
The concept of ARCH might be only a decade old, but its roots go far into the
past, possibly as far as Ba0chelier (190), who was the first to conduct a rigorous
study of the behaviour of speculative prices. There was then a period of long
silence. Mandelbrot (1963,1967) revived the interest in the time series
properties of asset prices with his theory that random variables with an
infinites population variance are indispensable for a workable description of
price changes. His observations, such as unconditional distributions have thick
tails, variance change over time and large(small) changes tend to be follow by
large(small) changes of either sign are stylized facts for many economic and
financial variables. Empirical evidence against the assumption of normality in
stock return has been ever since the pioneering articles by Mandelbrot (1963),
Fama (1965), and Clark (1973) which they argued that price changes can be
characterized by a stable Paretian distribution with a characteristic exponent
less than two, thus exhibiting fat tails and an infinite variance. Volatility
clustering and leptokurtosis are commonly observed in financial time series
(Mandelbrot, 1963). Another phenomenon often encountered is the so called
“leverage effect” (black 1976) which occur when stock price change are
negatively correlated with changes in volatility. Such studies is scared in
Nigeria Stock Exchange Market and observations of this type in financial time
series have led to the use of a wide range of varying variance models to
estimate and predict volatility.
In his seminal paper, Engle (1982) proposed to model time-varying
conditional variance with Autoregressive Conditional Heteroskedasticity
(ARCH) processes using lagged disturbances; Empirical evidence based on his
work showed that a high ARCH order is needed to capture the dynamic
behaviour of conditional variance. The Generalised ARCH (GARCH) model of
Bollerslev (1986) fulfils this requirement as it is based on an infinite ARCH

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