Partially adapting multi-step local linear prediction

An adaptive multi-step local linear prediction method is derived for nonlinear time series by partially updating the predictor with an implicit vector inner product involved in every prediction. The predictor mainly consists of two parts, the basic vector which is calculated at one step based on the nearest neighbors of the current state point, and the updating vector which ensures the validity of the multi-step prediction. Analyses on the precision and computational complexity are made with close comparisons with other prediction methods based on the local linear model. Straightforward performance comparisons made with the classical Lorenz series show that while preserving an admirable precision, the proposed method reduces the computational complexity, thus rendering it more applicable of real time signal processing than the others based on the local linear model. Experiments on voiced sounds are also made and the results demonstrate that, as compared with the traditional linear prediction (LP) method, a remarkable performance gain in precision is achieved with the proposed method, while the computations it costs are similar to that consumed by the LP method.