No abstract

Heatwaves are associated with increased mortality and are exacerbated by the urban heat island (UHI) effect. Thus, to inform climate change mitigation and adaptation, we quantified the mortality burden of historical heatwave days in Sydney, Australia, assessed the contribution of the UHI effect and used climate change projection data to estimate future health impacts. We also assessed the potential for tree cover to mitigate against the UHI effect. Mortality (2006–2018) records were linked with census population data, weather observations (1997–2016) and climate change projections to 2100. Heatwave-attributable excess deaths were calculated based on risk estimates from a published heatwave study of Sydney. High resolution satellite observations of UHI air temperature excesses and green cover were used to determine associated effects on heat-related mortality. These data show that >90% of heatwave days would not breach heatwave thresholds in Sydney if there were no UHI effect and that numbers of heatwave days could increase fourfold under the most extreme climate change scenario. We found that tree canopy reduces urban heat, and that widespread tree planting could offset the increases in heat-attributable deaths as climate warming progresses.

Generalized fractional processes in terms of Gegenbauer polynomials and GARCH (Generalized Autoregressive Conditional Heteroscedastic) errors is introduced and derived as a time series model. A related simulation study of the proposed model depicts statistical properties of the new class established in terms of the realization, sample autocorrelation function, theoretical autocorrelation function, partial autocorrelation function and the spectral density function

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 to 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 are provided.The above approach has been extended to model fractionally differenced Gegenbauer processes with conditional heteroskedastic errors and models with seasonality (see [1]). This paper motivated the development of the model in the thesis. Potential applications are provided. In addition, quasi-likelihood-type ratio tests have been developed for testing unit roots, stationarity versus nonstationarity and Gegenbauer long memory versus standard long memory.The results of the thesis have been reported in a series of working papers of the School of Mathematics and Statistics of the University of Sydney and in the papers [2,3].