Abstract
A general experimental description of chaotic phenomena is considered. A chaotic phenomenon is represented by an auto-regressive field whose evolution law is modeled by a non-linear mapping relation. This relation is formulated statistically by a conditional average estimator which is approximately calculated by nearest neighbor average. The structure of the model is expressed non-parametrically in terms of local state vectors which are reconstructed from data of recorded field. A novel reconstruction is presented using strongly and weakly correlated field values. The conditional average estimator is applicable for the prediction of field distribution outside some given initial domain on short and long scales. The method is demonstrated by predicting chaotic Kuramoto-Sivashinsky field and a turbulent vector field of ionization waves in plasma. The performance of statsitical modeling is estimated by comparing correlation functions of experimentally recorded and predicted fields.
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