New approaches to modeling volatility are evaluated and properties of partial least squares (PLS) regression are investigated. Common methods for modeling volatility, the standard deviation of price changes over a period, that account for the heavy tails of asset returns rely on maximum likelihood estimation using a heavy-tailed distribu- tion. A fractional power GARCH model is developed for robust volatility modeling of heavy tailed returns using a fractional power transform and Gaussian quasi maximum likelihood estimation. Furthermore, a smooth periodic GARCH model, incorporating seasonal trends by wavelet analysis, is developed and shown to outperform existing approaches in long-horizon volatility forecasting. PLS is a latent variable method for regression with correlated predictors. Previous approaches to derive the asymptotic covariance of PLS regression coefficients rely on restrictive assumptions. The asymptotic covariance of PLS coefficients are derived under general conditions. PLS regression is applied to variable selection in the context of index tracking.