The Nobel Memorial Prize for

Engle’s footsteps range widely. His major contributions include early work on band-spectral regression, development and unification of the theory of model specification tests (particularly Lagrange multiplier tests), clarification of the meaning of econometric exogeneity and its relationship to causality, and his later stunningly influential work on common trend modeling (cointegration) and volatility modeling (ARCH, short for AutoRegressive Conditional Heteroskedasticity). More generally, Engle’s cumulative work is a fine example of best-practice applied time-series econometrics: he identifies important dynamic economic phenomena, formulates precise and interesting questions about those phenomena, constructs sophisticated yet simple econometric models for measurement and testing, and consistently obtains results of widespread substantive interest in the scientific, policy and financial communities. Although many of Engle’s contributions are fundamental, I focus largely on the two most important: the theory and application of cointegration, and the theory and application of dynamic volatility models. Moreover, I discuss much more extensively Engle’s volatility models and their role in financial econometrics, for several reasons. First, Engle’s Nobel citation was explicitly ‘‘for methods of analyzing economic time series with time-varying volatility (ARCH)’’, whereas Granger’s was for ‘‘for methods of analyzing economic time series with common trends (cointegration)’’. Second, the credit for creating the ARCH model goes exclusively to Engle, whereas the original cointegration idea was Granger’s, notwithstanding Engle’s powerful and well-known contributions to the development. Third, volatility models are a key part of the financial econometrics theme that defines