Hong Pi and Carsten Peterson
Finding the embedding dimension and variable dependences in time
Neural Computation 6, 509-520 (1994)

We present a general method, the δ-test, which establishes functional dependencies given a sequence of measurements. The approach is based on calculating conditional probabilities from vector component distances. Imposing the requirement of continuity of the underlying function, the obtained values of the conditional probabilities carry information on the embedding dimension and variable dependencies. The power of the method is illustrated on synthetic time-series with different time-lag dependencies and noise levels and on the sunspot data. The virtue of the method for preprocessing data in the context of feed-forward neural networks is demonstrated. Also, its applicability for tracking residual errors in output units is stressed.

LU TP 93-04