The DFG collaborative research project 823 was devoted to non-linear dynamic processes in economics and engineering, with the aim of enlarging and improving the range of statistical models and methods in these fields. Time-scales ranged from milli-seconds in incremental sheet metal forming up to several years when modelling dynamic adjustment processes in economic macro contexts. Methodologically, projects were held together by newly developed models and methods in experimental design and time-series analysis. Important issues for projects in economics included time-varying dependence and risk structures in finance, new industrial production functions with a special view on energy inputs, or new specifications of the role of labour as an input in production-processes. Projects in engineering were concerned with optimizing thermal spraying by taking account of complex interactions among e.g. temperature, speed and intensity of particles, the drilling in concrete or the processing of music signals in hearing aids. This research built heavily on methodological advances in experimental design and inverse problems, and on newly developed independent component models. Further methodological progress initiated by SFB 823 includes new copula-models plus a variety of useful tests and quantile regression with timevariable inputs and components; such models have become important tools both in engineering and economics recently. The multitude of topics investigated was united under the common roof of dynamic models, resulting in fruitful cross-fertilization und important mutual inspirations. In addition, a series of high level conferences has secured a strong foundation in the international research community. Various fruitful collaborations which were initiated here will survive SFB 823 and may be viewed as part of its scientific legacy. 

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