Grant: Discovery Grants Program - Individual

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. The statistical properties of interest are moment properties, hypothesis testing, smoothing and forecasting of non-linear generalized autoregressive conditional heteroscedastic (GARCH) models. In order for valid conclusions to be drawn from statistical modelling, the underlying model assumptions need to be satisfied. I propose to investigate data-driven methods for testing whether the model assumptions have been met. For example, the moment properties such as the autocorrelation of the squared process of the kurtosis can be used to identify the appropriate model. Hypothesis tests allow the analyst to quantify the uncertainty about model parameters while smoothing of estimates based on volatility models allows for improvements in estimation. Derivation of forecasts and their standard errors allows for future prediction of volatility assuming the current economic conditions persist. By gaining insight into the statistical properties of volatility models, analysts will be better equipped to make informative decisions in financial practice.