This paper describes the fundamental change in paradigm in time series prediction that has occurred in the last decade. The examples are drawn from the Santa Fe Time Series Prediction and Analysis Competition. In 1979, the results of an earlier competition were published by the Royal Society. In that competition, and also in the follow up five years later, relatively large numbers of time series were provided (111 and 1001, respectively), taken from business (forecasting sales), economics (predicting recovery from the recession), finance, and the social sciences. However, all of the series used were very short, generally less than 100 values long. Most of the algorithms entered were fully automated, and most of the discussion centred around linear models. In contrast, the Santa Fe Competition focused on only six data-sets, ranging from 1000 to 100 000 points. All of the successful entries were fundamentally nonlinear and, even though significantly more computer power was used to analyse the larger data-sets with more complex models, the application of the techniques required more careful manual control than in the past. There was a general failure of simplistic `black-box' approaches. In all successful entries, exploratory data analysis preceded the application of the algorithm. The Santa Fe Competition showed examples of nonlinear results going far beyond what is possible within the canon of linear systems analysis, but also showed that there are unprecedented opportunities for the analysis to go astray.