A Potential Method for Determining Nonlinearity in Wind Data

This paper investigates a basic problem in modeling time series of wind data: whether there exists detectable correlation or nonlinearity in the observed wind time series. At present, a variety of linear and nonlinear time series models have been applied to predict the wind data. The first question that should be answered before building a model, however, is whether the data studied are correlated or carry nonlinearity. It would be futile to model the relationships if the pertaining wind data cannot be distinguished from the white noise. Advanced nonlinear prediction models are also not necessary if there are no nonlinear structures in the data. In this paper, we test by the surrogate data method: 1) whether the differenced wind speed time series (taking the first difference of the time series) is white noise, and 2) the presence of nonlinearity in the original wind speed time series. Nine data sets, including 10 min and hourly wind speed data, are examined. The results show that all of the differenced wind speed time series are correlated, and three out of the nine original wind speed time series satisfy the hypothesis of a linear stochastic generating process. It is concluded that for a specific wind speed time series, the nonlinearity is data-dependent from the perspective of practical time series analysis.