This collection of original articles-8 years in the making-shines a bright light on recent advances in financial econometrics. From a survey of mathematical and statistical tools for understanding nonlinear Markov processes to an exploration of the time-series evolution of the risk-return tradeoff for stock market investment, noted scholars Yacine A̐t-Sahalia and Lars Peter Hansen benchmark the current state of knowledge while contributors build a framework for its growth. Whether in the presence of statistical uncertainty or the proven advantages and limitations of value at risk models, readers will discover that they can set few constraints on the value of this long-awaited volume. Presents a broad survey of current research-from local characterizations of the Markov process dynamics to financial market trading activity. Contributors include Nobel Prize laureate Robert Engle and other leading econometricians Offers a clarity of method and explanation unavailable in other financial econometrics collections.