American Statistical Association New York City Metropolitan Area Chapter Mailman School of Public Health Columbia University Department of Biostatistics Colloquium

Generalized integrated processes were introduced by Granger in 1998. From a statistical viewpoint, they extend the fractional autoregressive moving average processes used in time series analysis, and, from a probabilistic viewpoint, they extend the classical random walk to fractional analogues. In this talk, I will give an overview of the little we know and a glimpse of what we would like to know about those processes when they have no stationary solutions. I will explain why I find them interesting both for modeling and theoretical investigations. I will indicate open problems, share questions, doubts and uncertainties.

Philippe Barbe has a degree in applied statistics from ENSAE and a Ph.D. in statistics from the University of Paris 6. He was appointed at the CNRS in 1993 and held several visiting positions in Europe and in the US. His work covers various areas of statistics and applied probability, mostly guided by his interests of the moment and scientific encounters.