Finding the embedding dimension and variable dependencies in time series

Research output: Contribution to journalArticle


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 feedforward neural networks is demonstrated. Also, its applicability for tracking residual errors in output units is stressed.


  • Hong Pi
  • Carsten Peterson
External organisations
  • Lund University
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Other Physics Topics
Original languageEnglish
Pages (from-to)509-520
Number of pages11
JournalNeural Computation
Issue number3
Publication statusPublished - 1994
Publication categoryResearch