Advances in computational power and data storage have spawned a new research area in financial economics and statistics called high-frequency finance. The defining feature of high-frequency finance is the analysis of financial processes over short intraday time horizons. This time horizon may be the trade-by-trade behavior of the market, or it may be locally aggregated behavior over intraday intervals. The analysis of intraday financial processes is motivated by the micro-foundations of aggregate market behavior. It is hoped that micro-level market properties can help explain macro-level market properties. Two topics of particular interest are the statistical modeling of these intraday processes and the temporal aggregation of these intraday statistical models. This dissertation examines the statistical modeling of intraday trading dynamics. The particular aspect of trading dynamics of interest is the relationship between the trade and quote processes. The affect of trading activity on quoting behavior is one of the central problems in the economic theory of market microstructure. In order to investigate this relationship at the transaction level, the dynamics of the trade and quote processes for eight securities traded on the New York Stock Exchange (NYSE) are modeled in a market microstructure framework. We begin by defining the EL Model and the EL Model framework developed in Engle and Lunde (2003). We propose an alternative to the EL Model for the modeling of trade and quote dynamics using the Cox regression model. The Cox regression model has many data analytic advantages. With the Cox regression model we are able to perform a thorough statistical analysis of transaction level trade and quote behavior. We conclude by investigating a local Poisson approximation of intraday trade and quote behavior in five minute intervals using the Poisson generalized linear model with dispersion.