This dissertation explores the potential for non-parametric estimation of conditional variation in financial markets. We suggest that these tools are useful given the lack of theoretical foundations and the lack of consensus on the proper data-generating mechanism of financial returns. The results obtained in this way could then become the basis for future modelling efforts. In this vain, we first develop a non-parametric test for jumps in the conditional variance and show that financial returns are subject to such jumps. Secondly, we analyze the relation between financial returns and their associated risk which we measure as a non-parametric estimate of their variance. We extend weak instrument asymptotic theory to analyze this relationship and argue that it provides a better approximation for financial data. This leads us to conclude that no significant statistical relationship exists between the first two moments for the series we analyze. Finally, we carry out a small-scale simulation experiment which suggests that persistence should be the key determinant in the choice of the non-parametric technique to use to estimate the conditional variance. Together, these results provide the basis for future application of non-parametric estimation in this setting and suggest future directions for the modelling of financial returns.
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