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Abstract:
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The classical methods of analysing time series by Box-Jenkins approach assume that
the observed series
uctuates around changing levels with constant variance. That
is, the time series is assumed to be of homoscedastic nature. However, the nancial
time series exhibits the presence of heteroscedasticity in the sense that, it possesses
non-constant conditional variance given the past observations. So, the analysis of
nancial time series, requires the modelling of such variances, which may depend
on some time dependent factors or its own past values. This lead to introduction of
several classes of models to study the behaviour of nancial time series. See Taylor
(1986), Tsay (2005), Rachev et al. (2007). The class of models, used to describe
the evolution of conditional variances is referred to as stochastic volatility modelsThe stochastic models available to analyse the conditional variances, are based on
either normal or log-normal distributions.
One of the objectives of the present study is to explore the possibility of employing
some non-Gaussian distributions to model the volatility sequences and then study
the behaviour of the resulting return series. This lead us to work on the related
problem of statistical inference, which is the main contribution of the thesis |