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The main theme of this dissertation is multivariate modeling in financial econometrics. The first chapter uses the fundamental properties of the multivariate distributions of independent random variables to develop a new specification testing methodology for dynamic models. The second chapter generalizes this methodology to tests of distributional assumptions and dynamic specification in multivariate models. In the third chapter we focus on testing and modeling asymmetries in the second moments of multiple equity returns.The methodological advances in nonlinear time series models with non-normal density functions and in density forecasting have emphasized the need for developing dynamic specification tests for the joint hypothesis of i.i.d.-ness and density functional form. In Chapter I, we propose a new battery of tests that rely on the fundamental properties of independent random variables with identical distributions and we introduce a graphical device -the autocontour-that helps to visualize the modeling problems. Based on the theoretical probability coverage of the autocontours, we construct a battery of asymptotic t-tests and chi-squared tests, which have standard convergence rates. The tests are very powerful against violations of both hypotheses. They do not require either a transformation of the original data or an assessment of goodness-of-fit à-la Kolmogorov and explicitly account for parameter uncertainty. Monte Carlo simulations show that their finite sample performance is very good even in relatively small samples. We illustrate the usefulness of this methodology within the context of GARCH and ACD models using returns and duration data from the US equity markets.In Chapter II, we generalize the testing methodology developed in Chapter I to time series models with multivariate GARCH disturbances. The tests are applied to the vector of generalized errors that must be i.i.d. with a certain parametric multivariate probability density function under the null hypothesis of correct specification. We develop t-tests based on a single autocontour and also more powerful chi-squared tests based on multiple autocontours. In the spirit of goodness-of-fit tests, we also propose an additional test that focuses on the multivariate density functional form of the vector of innovations. We perform Monte-Carlo simulations to investigate the size and power properties of the test statistics in finite samples. We apply our tests to multivariate GARCH models fitted to excess returns on portfolios sorted according to market capitalization.In Chapter III we test and model asymmetries in time-varying means, volatilities, correlations, and betas of equity returns in a multivariate threshold framework. We consider alternative specifications in which the threshold variable is based on market excess return, the Fama-French size and value factors, realized volatility of the market portfolio, and variables reflecting economic fundamentals. We find strong threshold effects with respect to market excess return, value premium, and term spread. Our results indicate that the threshold model based on market excess return provides a flexible and computationally inexpensive specification for modeling asymmetries, especially when dimensionality is high. We find that small caps, value stocks, and the Durables industry exhibit the strongest expected return asymmetries. Correlations of small caps, value firms, and defensive industries with the market tend to be significantly larger during market downturns. Correlation asymmetry usually translates into asymmetry in beta. Regime dependent volatility is a common characteristic of all portfolio groups. We evaluate performance of the proposed threshold models in an out-of-sample setup and find that there can be substantial economic gains in incorporating asymmetries in portfolio decisions.