ABSTRACT
This chapter introduces stochastic processes that can be used to model data with the properties. Qualitative features of a typical sample path; there are relatively long periods where the observations tend to stay at a high level there are long periods with low levels. The chapter looks at short time periods, then there seem to be cycles or local trends. It also looks at the whole series, there is no apparent persisting trend or cycle. It rather seems that cycles of all frequencies occur, superimposed and in random sequence and Overall, the series looks stationary. Self-similar processes were introduced by A. N. Kolmogorov in a theoretical context. Statisticians do not seem to have been aware of the existence or statistical relevance of such processes, until Mandelbrot and his co-workers. The basic idea of self-similarity is much older. B. B. Mandelbrot refered to Leonardo da Vinci's drawings of turbulent flows that exhibit coexistent "eddies" of all sizes and thus self-similarity.
