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|dc.description.abstract||The class of long memory time series models involving Gegenbauer processes is
investigated in detail in terms of formulation, parameter estimation, prediction and
testing. Corresponding truncated AR (autoregressive) and MA (moving average)
approximations driven by Gaussian white noise are analysed through state space
modelling and Kalman filtering to assess the viability of estimating techniques .
The optimal approximation option is employed to proceed with the estimation of
model parameters. The resulting mean square errors are validated by the predictive
accuracy to establish an optimal lag order through a large scale simulation study. It
is shown that the use of this newly established lag order for a real data application
provides benchmarks which are comparable and mostly better than a number of
existing results in the literature. It is followed by an execution of this technique to
extract and assess seasonal models through a Monte Carlo experiment. Thereafter empirical applications were provided.
The above approach has been extended to model fractionally differenced Gegenbauer processes with conditional heteroskedastic errors and models with seasonality. Potential applications are provided. In addition, quasi-likelihood type ratio tests have been developed for testing unit roots, stationarity versus non-stationarity and Gegenbauer long memory versus standard long memory.||en_AU|
|dc.publisher||University of Sydney.||en_AU|
|dc.publisher||School of Mathematics & Statistics.||en_AU|
|dc.title||Advancement of Fractionally Differenced Gegenbauer Processes with Long Memory||en_AU|
|dc.type.pubtype||Doctor of Philosophy Ph.D.||en_AU|
|Appears in Collections:||Sydney Digital Theses (Open Access)|
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|2015_Gnanadarsha_Dissanayake_Thesis.pdf||PhD Thesis||1.04 MB||Adobe PDF|
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