Inference using estimating functions with applications

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Volatility modelling has implications for asset pricing, optimal portfolio theory and risk management. Volatility or the instantaneous rate of return of the underlying security was assumed to be constant up until 1982. Ever since Robert F. Engle recognized the time-varying nature of volatility in 1982, there has been extensive research into extending his class of autoregressive conditional heteroscedastic (ARCH) models to incorporate additional salient features of financial returns data. Engle's recognition of the time-varying nature of volatility has made a significant impact in the theory of economics. However, many statistical properties of the models proposed in volatility modelling research have yet to be studied and provide a wealth of research opportunities.