Time series

Sequences of continuous numerical data are often known as time series, and starting in the 1960s standard models for them have consisted of linear recurrence relations or linear differential equations with random noise continually being added. The linearity of such models has allowed efficient methods for estimating their parameters to be developed, and these are widely used, under slightly different names, in control engineering and in business analysis. In recent years nonlinear models have also sometimes been considered, but typically their parameters are very difficult to estimate reliably. As discussed on page 919 it was already realized in the 1970s that even without external random noise nonlinear models could produce time series with seemingly random features. But confusion about the importance of sensitivity to initial conditions caused the kind of discoveries made in this book to be missed.