Quantizing the deterministic nonlinearity in wind speed time series

Linear models are capable of capturing the Linear Deterministic (LD) component of the time series. In order to benefit from both Nonlinear Deterministic (ND) and LD components during the prediction procedure, it is necessary to employ nonlinear models. The complexity of the prediction algorithm increases when nonlinear models are utilized. Hence, before applying nonlinear models the presence of nonlinear component should be confirmed. Although surrogate data technique uses various tests to indicate the nonlinearity, in many cases its test results are different and in conflict with each other. The reason is time series include LD and ND components together and giving a strict answer about nonlinearity cannot be applicable. Here instead of such a strict answer, by quantizing the ND component, a new index (a number between 0 and 1) is proposed (the closer to 1 the more ND components). In this method first we use ARMA models. The residual series is used to calculate the proposed index which it contains all components of the original series except LD. The proposed procedure is applied to three different case studies. Furthermore, the performance of some nonlinear prediction methods (Markov, Grey, Grey–Markov, EMD–Grey, NARnet and ARMAX) is compared with the proposed index.