Nonlinear prediction of near-surface temperature via univariate and multivariate time series embedding

Surface temperature is an important variable, especially for frost prediction and other agricultural applications. For these purposes, accurate surface temperature measurements or predictions are required. The present study uses univariate (UTSE) and multivariate time series embedding (MTSE) for the purpose of nonlinear time series prediction. These two approaches require multidimensional phase space construction. The coordinates of this space are spanned by the time series itself and its shifted versions. Then the prediction is performed by estimating the change in trajectory by a polynomial approximation. In univariate time series embedding, prediction of the soil temperatures measured at 2 cm below the soil surface was performed. In multivariate time series embedding, air temperature and wind speed data were used together with the soil temperature. Predictions obtained from the UTSE and the MTSE were compared with conventional methods such as AR(p) and multivariate AR(p). Errors between the observed and the predicted values are slightly smaller than those of the conventional methods.