This dissertation consists of four papers that examine various aspects of the temporal patterns in the volatility of asset returns. The first paper compares the predictive performance of various parametric ARCH models. We find that ARCH models are generally good descriptions of the timevarying volatility of UK stock returns. There appears to be asymmetry in the conditional volatility, although no single model outperforms the rest in all instances. In the second paper, we uncover evidence of asymmetric predictability in the conditional variance of firms of different size. Large firms shocks affect the future volatility of small firms, but not vice versa. We also find that trading period shocks have a significant impact on future volatility, but not nontrading period shocks. In the third paper, we document a contemporaneous volatility-volume relationship. We find that volatility is related to change in trading volume, and we propose a conditional volatility model that incorporate this contemporaneous volatility-volume relationship. In the final paper, we examine the various method of adjusting for nontrading effects in ARCH models, and we propose a new diagnostic test to detect the validity of such adjustments. We also uncover evidence that conditional volatility increases prior to market closure, but declines after market opening.