Richard Davis is the Howard Levene Professor of Statistics and Chair of the Statistics Department at Columbia University. He received his Ph.D. degree in Mathematics from the University of California at San Diego in 1979, where he worked under the guidance of Murray Rosenblatt. His thesis work centered on extreme value theory applied to stationary processes. After graduate school, he joined the Statistics Group in the Mathematics Department at MIT where he worked under the direction of Herman Chernoff. In 1981, he joined the Statistics Department at Colorado State University, where he served for an extended period as the department’s chair (1997 —2005). In 2007, Davis was recruited to Columbia University, to become the Howard Levene Professor of Statistics, a position he still holds. For the past five years, he has chaired the statistics department at Columbia.

In his PhD work, Davis worked on problems related to limit theory for extremes of a stationary time series. A key aspect of this work was the clustering of extremes due to the serial dependence. In joint work with Resnick, Davis laid out the behavior of extremes for heavy tailed linear processes. Their seminal 1984 laid out a powerful point process technique that applied to linear processes which was subsequently used to establish a number of limit results for other statistics besides the extremes. Specifically, the (1985) and (1986) papers laid out the limit theory for the sample correlation of linear time series models with infinite variance. Although this paper is some 33 years old, the techniques derived in this paper are still being used today in the multivariate setting. In follow-up work, Davis and Hsing (1995) employed point process convergence methods for what they called heavy-tailed time series. These are time series, for which all the finite-dimensional joint

istributions are heavy-tailed, an assumption that nowadays is commonly made. This paper led the way to an important work on limit behavior for extremes,

sample correlations, and even MLE in many nonlinear time series models including GARCH and SV processes. Much of this work was collaborative with Thomas Mikosch and students. In recent years, this line of research expanded to study the sample cross-correlation matrix of heavy-tailed multivariate time series. Davis and Mikosch were able to establish the limit behavior of the extreme sample eigenvalues when the dimension of the series p grew with the sample size. These were the first results of this kind.

Inspired by Rosenblatt, Davis has also been interested in non-causal/non-invertible ARMA models for a number of years, where he has made a number of important contributions. In particular, he studied all-pass models which are linear processes that exhibit nonlinear behavior. Together with co-authors, he developed a model identification/estimation paradigm for these processes which play a key role in studying non-causal models. Interestingly, noncausal models have made recent appearances in the study of financial bubbles.

In 1996, Davis and Dunsmuir cracked the problem of establishing the limit behavior of the maximum likelihood estimator of the MA(1) parameter when there is a unit root. This result, which eluded many of the experts in the field and the resulting paper received the Koopmans Econometric Theory Prize in 1997 with the citation, “The paper solves one of the last open questions in the asymptotic theory of likelihood for ARMA models.”

Davis and Dunsmuir have done fundamental work on developing models for times series of counts. They established some of the important theory results needed to justify the use of the major inference procedures.

In addition to these topics, Davis has made key contributions to a wide range of time series and spatial modeling problems that include: structural break estimation: spatial modeling with applications to environmental statistics and computer experiments; continuous-time modeling with applications to high-frequency return data; with applications to environmental, medical, space-time modeling of extremes, financial time series, high-dimensional and sparse VAR models, etc.

Davis is coauthor (with P.J. Brockwell) of the best-selling books on time series analysis, Time Series: Theory and Methods, (Springer-Verlag, 1987, 2nd ed., 1991, paperback in 2009, Chinese translation in 2001) and Introduction to Time Series and Forecasting, (Springer-Verlag, 1996, 2nd ed., 2002, 3rd ed. 2016, Japanese translation 1999). The former is the standard reference in the field and both are commonly used as texts worldwide. He also co-edited (with Andersen, Kreiss, and Mikosch), the well-regarded Handbook of Financial Time Series in 2009. In 2016, Davis co-edited with Holan, Lund and Ravishanker, the Handbook of Discrete-Valued Time Series.

He has served on the editorial boards of major journals in probability and statistics and was Editor-in-Chief of the Bernoulli Journal, 2010-2012. Recently he was Hans Fischer Senior Fellow at the Technical University of Munich and Villum Kan Rasmussen Visiting Professor at the University of Copenhagen. He is a fellow of the American Statistical Association and the Institute of Mathematical Statistics, and is an elected member of the International Statistics Institute. In 2016, he served as President of IMS, the largest professional society for statisticians and probabilists. On top of his research and heavy service roles at the department, university and

professional levels, he has mentored a number of postdoctoral fellows and has advised/coadvised 33 PhD students.