# Kolmogorov Space in Time Series Data

**Authors:** K. Kanjamapornkul, R. Pinčák  
**arXiv:** [1606.03901](https://arxiv.org/abs/1606.03901)  
**Date:** 2016-06-10  
**Summary page:** https://www.summarizepaper.com/en/paper/1606.03901v1/

## Key points

- Authors K. Kanjamapornkul and R. Pinčák introduce a novel approach to analyzing time series data using Kolmogorov space
- The space of time series data exhibits properties of a Kolmogorov space with $T_{0}$-separation axiom
- Unique concept of defining a cyclic coordinate representing intrinsic time scale after empirical mode decomposition
- Introduction of spinor field derived from rotating data around price and time axes for extradimensional perspective
- Revelation of hidden eight dimensions within Kolmogorov space when applied to time series data
- Practical implementation demonstrated through algorithms like empirical mode decomposition and intrinsic time scale decomposition

## Summary

In their paper titled "Kolmogorov Space in Time Series Data," authors K. Kanjamapornkul and R. Pinčák present a novel approach to analyzing time series data within the framework of Kolmogorov space. They provide a rigorous proof that the space of time series data exhibits the properties of a Kolmogorov space with $T_{0}$-separation axiom by utilizing the loop space of time series data. This demonstrates the applicability and effectiveness of using Kolmogorov space as a tool for analyzing temporal datasets. The authors introduce a unique concept of defining a cyclic coordinate representing the intrinsic time scale of time series data after applying empirical mode decomposition. This allows for a deeper understanding of the underlying structure and dynamics within the data, providing valuable insights into its complex relationships. Additionally, they introduce a spinor field derived from rotating data around price and time axes, introducing a new extradimensional perspective to time series analysis. This innovative approach adds another layer to traditional methods and offers potential for further exploration in various fields such as finance, economics, and signal processing. One of the key contributions of this work is the revelation that there exist hidden eight dimensions within Kolmogorov space when applied to time series data. By leveraging algorithms such as empirical mode decomposition and intrinsic time scale decomposition, the authors demonstrate how this concept can be practically implemented for preliminary analysis on real-world datasets. Overall, this study offers a fresh perspective on analyzing time series data through the lens of Kolmogorov space. Its findings have implications for various fields where accurate modeling and prediction based on historical trends are crucial.