Embedology and Neural Estimation for Time Series Prediction

Time series prediction has widespread application, ranging from predicting the stock market to trying to predict future locations of scud missiles. Recent work by Sauer and Casdagli has developed into the embedology theorem, which sets forth the procedures for state space manipulation and reconstruction for time series prediction. This includes embedding the time series into a higher dimensional space in order to form an attractor, a structure defined by the embedded vectors. Embedology is combined with neural technologies in an effort to create a more accurate prediction algorithm. These algorithms consist of embedology, neural networks, Euclidean space nearest neighbors, and spectral estimation techniques in an effort to surpass the prediction accuracy of conventional methods. Local linear training methods are also examined through the use of the nearest neighbors as the training set for a neural network. Fusion methodologies are also examined in an attempt to combine several algorithms in order to increase prediction accuracy. The results of these experiments determine that the neural network algorithms have the best individual prediction accuracies, and both fusion methodologies can determine the best performance. The performance of the nearest neighbor trained neural network validates the applicability of the local linear training set