Peter Craigmile's research interests include time series analysis, spatial statistics, space-time modeling, and longitudinal methods. He is interested in the use of spectral and wavelet methods to investigate dependency structures and to analyze periodicities and trends. One application of this is to the study of long memory processes. He also works on methodology for spatial extrema and exceedances. He enjoys application-oriented research in areas such as Climatology, Environmental Sciences, and Psychology.
He is a fellow of the American Statistical Association and The Royal Statistical Society. He is a member of the Institute of Mathematical Statistics, the International Environmetrics Society, the International Society for Bayesian Analysis, and the Edinburgh Mathematical Society.