We investigate two open problems in the area of time series analysis. The first is developing a methodology for multivariate time series analysis when our time series has components that are both continuous and categorical. Our specific contribution is a logistic smooth transition regression (LSTR) model whose transition variable is related to a categorical variable. This methodology is necessary for series that exhibit nonlinear behavior dependent on a categorical variable. The estimation procedure is investigated both with simulation and an economic example. The second contribution to time series analysis is examining the evolving structure in multivariate time series. The application area we concentrate on is financial time series. Many models exist for the joint analysis of several financial instruments such as securities due to the fact that they are not independent. These models often assume some type of constant behavior between the instruments over the time period of analysis. Instead of imposing this assumption, we are interested in understanding the dynamic covariance structure in our multivariate financial time series, which will provide us with an understanding of changing market conditions. In order to achieve this understanding, we first develop a multivariate model for the conditional covariance and then examine that estimate for changing structure using multivariate techniques. Specifically, we simultaneously model individual stock data that belong to one of three market sectors and examine the behavior of the market as a whole as well as the behavior of the sectors. Our aims are detecting and forecasting unusual changes in the system, such as market collapses and outliers, and understanding the issue of portfolio diversification in multivariate financial series from different industry sectors. The motivation for this research concerns portfolio diversification. The false assumption that investment in different industry sectors is uncorrelated is not made. Instead, we assume that the comovement of stocks within and between sectors changes with market conditions. Some of these market conditions include market crashes or collapses and common external influences.