The primary objective of this dissertation is to extend the classical Principal Components Analysis (PCA), aiming to reduce the dimensionality of a large number of Normal interrelated variables, in two directions. The first is to go beyond the static (contemporaneous or synchronous) covariance matrix among these interrelated variables to include certain forms of temporal (over time) dependence. The second direction takes the form of extending the PCA model beyond the Normal multivariate distribution to the Elliptically Symmetric family of distributions, which includes the Normal, the Student's t, the Laplace and the Pearson type II distributions as special cases. The result of these extensions is called the Generalized principal component analysis (GPCA). The GPCA is illustrated using both Monte Carlo simulations as well as an empirical study, in an attempt to demonstrate the enhanced reliability of these more general factor models in the context of out-of-sample forecasting. The empirical study examines the predictive capacity of the GPCA method in the context of Exchange Rate Forecasting, showing how the GPCA method dominates forecasts based on existing standard methods, including the random walk models, with or without including macroeconomic fundamentals. / Ph. D. / Factor models are employed to capture the hidden factors behind the movement among a set of variables. It uses the variation and co-variation between these variables to construct a fewer latent variables that can explain the variation in the data in hand. The principal component analysis (PCA) is the most popular among these factor models. I have developed new Factor models that are employed to reduce the dimensionality of a large set of data by extracting a small number of independent/latent factors which represent a large proportion of the variability in the particular data set. These factor models, called the generalized principal component analysis (GPCA), are extensions of the classical principal component analysis (PCA), which can account for both contemporaneous and temporal dependence based on non-Gaussian multivariate distributions. Using Monte Carlo simulations along with an empirical study, I demonstrate the enhanced reliability of my methodology in the context of out-of-sample forecasting. In the empirical study, I examine the predictability power of the GPCA method in the context of “Exchange Rate Forecasting”. I find that the GPCA method dominates forecasts based on existing standard methods as well as random walk models, with or without including macroeconomic fundamentals.