Multidimensional Embedding and Nearest Neighbour Algorithm for Prediction

Based on the fractal model of dynamic swings and the wavelet analysis of physical cycles in a quantum space of price and time, we will investigate two different approaches for predicting the stock index movement The first is a direct application of the fractal model and wavelet analysis whose parameters are estimated from the historical data, especially the last and current Elliott waves.

The second approach is a pattern recognition approach based on chaos theory. Each time sample from historical time series data is embedded in a multidimensional feature space, where the feature vector consists of a subset of the fractal and wavelet parameters, especially the phases at the multiple time scales.

For any given current time, its feature vector is constructed from the fractal and wavelet models, and then a certain number of its nearest neighbors are searched out from the historical pattern space. Finally, a certain nonlinear regression model can be estimated from the nearest neighbors. This model then can be used for prediction.

Note that this regression is local to the nearest neighbors, and thus the predictive model is adaptive.

Prof. Heping Pan