Multi-fractal detrended cross-correlation heatmaps for time series analysis

Area of Science:

• Complex Systems Analysis
• Economic Data Science
• Time Series Analysis

Background:

• Complex systems display emergent properties like non-linearity and self-organization, arising from interconnected components.
• Understanding these systems requires analyzing cross-correlations in time series data, which can be challenging due to multiscale structures and non-linear processes.
• Existing methods struggle to fully capture the intricate relationships and cyclical patterns within complex, non-stationary signals.

Purpose of the Study:

• To introduce a novel systematic approach, Multifractal detrended cross-correlation heatmaps (MF-DCCHM), for mapping relationships between signal fluctuations across different scales and regimes.
• To analyze cross-correlations and identify cyclical patterns in economic and sales data from the Brazilian automotive sector.
• To quantify the relationships between non-stationary signals while effectively removing noise.

Main Methods:

• Development and application of Multifractal detrended cross-correlation heatmaps (MF-DCCHM) utilizing DCCA cross-correlation coefficients and sliding boxes.
• Integration of time series magnitudes and averaging DCCA coefficients for local analysis on heatmaps.
• Utilized sales, inventory data from the Brazilian automotive sector, and macroeconomic indicators (GDP per capita, Nominal Exchange Rate, Nominal Interest Rate).

Main Results:

• MF-DCCHM successfully mapped cross-correlated patterns comparable to power-law spectra across multiple regimes.
• Identified cyclical patterns with high intensity coinciding with Brazilian presidential election periods.
• The heatmaps revealed consistent cyclical frequencies with spectral analysis across various multifractal regimes.

Conclusions:

• MF-DCCHM is a powerful tool for uncovering non-explicit cyclic patterns and quantifying relationships between non-stationary signals.
• The method effectively removes noise, providing clearer insights into complex system dynamics.
• MF-DCCHM demonstrates significant potential for mapping cross-regime patterns across diverse scientific and economic domains.