The thesis consists of four independent essays. Each discusses different applications of the Mixed Data Sampling (MIDAS) regression framework. The first essay explores MIDAS regression models. The models use time series data sampled at different frequencies. Volatility and related processes are the prime focus, though the regression method has wider applications in macroeconomics and finance, among other areas. The regressions combine recent developments regarding estimation of volatility and a not so recent literature on distributed lag models. Various lag structures to parameterize parsimoniously the regressions and relate them to existing models are studied and several new extensions of the MIDAS framework are proposed. The second investigates the response of daily U.S. firm returns to macroeconomic and firm-specific shocks. Because daily firm returns are inherently noisy, most previous papers that link economic fluctuations to stock returns do so at the market (or some other aggregate) level. The MIDAS approach allows addressing the noise issue by parameterizing the response to news as a parsimonious, flexible and simple function. The parameterization has two goals: it shrinks the noisy responses by implicitly imposing smoothness constraints and also reduces the number of coefficients to estimate. This method allows capturing many effects at once. The third essay assesses to what extend correction for microstructure noise improves forecasting future volatility using the MIDAS framework. It starts by studying the population properties of predictions using various realized volatility measures. It does this in a general regression setting and with both i.i.d. as well as dependent microstructure noise. Next it studies optimal sampling issues theoretically, when the objective is forecasting and microstructure noise contaminates realized volatility. The fourth essay addresses the issues of estimating and forecasting of volatility matrices which, because of their practical relevance, are central to Financial Econometrics. The application of classical multivariate methods to large dimensions is hampered by the curse of dimensionality. In this chapter a multivariate factor MIDAS model is developed, that offers a solution to the dimensionality problem and utilizes intraperiod information. The study extends the univariate MIDAS-based volatility model introduced by Ghysels, Santa-Clara and Valkanov.