Forecasting
In this section, we apply both linear and nonlinear forecast methods to the data in order to compare the accuracy of different methods. In this way, we aim to gain some insight into the dynamics of the generating process and to evaluate the forecast methods for this application. We apply several different linear and nonlinear forecasting methods, whose details are given in Additional file 1: Section II.
Table 3 shows the out-of-sample forecast results using linear and nonlinear time series methods. The methods are persistence PST, simple exponential smoothing SES, autoregression AR1 and AR2, Gaussian process regression MAT2, locally constant prediction LCP and local linear prediction LLP. There is little difference in accuracy between the forecasting methods. The range in error between the most and least accurate methods is less than 0.5 of a rating unit. A Deibold-Mariono test ([Diebold and Mariano 2002]) shows that for half the patients, none of the methods, including nonlinear methods, has more predictive accuracy than persistence forecasting. Full details of the test and results are given in Additional file 1: Section III.