Structure of memory in time series: A one-dimensional atomic chain model

Area of Science:

• Complex Systems
• Time Series Analysis
• Network Science

Background:

• Current time series analysis methods often lose crucial memory structure.
• Preserving detailed memory is essential for accurate time series modeling.

Purpose of the Study:

• To introduce a memory structure network for preserving time series memory.
• To analyze the spectral properties of this network for time series representation.

Main Methods:

• Extracting all possible segments from time series and mapping them to network nodes.
• Assigning dependence between node pairs as edge weights.
• Representing memory in a multi-dimensional space via spectral properties of the adjacency matrix.

Main Results:

• The spectral distribution of the memory structure network follows a beta-distribution.
• The network accurately captures the spectral behaviors of the Shanghai Stock Exchange Composite index, outperforming fBm and ARCH models.
• Symmetry-resolved sub-spectra follow a Weibull distribution, with repulsion effects linked to persistence and variance fluctuations.

Conclusions:

• The memory structure network effectively preserves and analyzes time series memory.
• Spectral analysis of the network provides insights into long-term persistence and variance dynamics.
• This approach offers a new perspective on interpreting memory exponents in time series.