A novel way to detect correlations on multi-time scales, with temporal evolution and for multi-variables

Area of Science:

• Complex Systems Analysis
• Time Series Correlation
• Climate Science

Background:

• Traditional correlation methods often fail to capture dynamic relationships in complex systems.
• Understanding temporal variations in correlations is crucial for accurate climate modeling and prediction.

Purpose of the Study:

• To introduce novel methods, Temporal evolution of Detrended Cross-Correlation Analysis (TDCCA) and Temporal evolution of Detrended Partial-Cross-Correlation Analysis (TDPCCA).
• To enable the study of correlations across multiple time scales and varying historical periods.
• To develop an improved correlation-detection system for complex time series.

Main Methods:

• Generalizing Detrended Cross-Correlation Analysis (DCCA) and Detrended Partial-Cross-Correlation Analysis (DPCCA) to their temporal evolution variants (TDCCA/TDPCCA).
• Applying TDCCA/TDPCCA to climatological data, specifically Global Sea Level (GSL) vs. North Atlantic Oscillation (NAO) and Summer Rainfall over Yangtze River (SRYR) vs. Pacific Decadal Oscillation (PDO).
• Integrating TDCCA/TDPCCA with DCCA/DPCCA to create a comprehensive correlation-detection system.

Main Results:

• Significant correlations between GSL and NAO were identified on time scales of 60-140 years, with non-significant periods observed (e.g., 1865-1875).
• Significant correlations between SRYR and PDO were found on time scales of 30-35 years, particularly pronounced in the last 30 years.
• The new system objectively quantifies the time scale and period of correlations between time series.

Conclusions:

• TDCCA and TDPCCA provide powerful tools for analyzing dynamic correlations in complex systems.
• The developed correlation-detection system offers objective insights into time series relationships, surpassing traditional methods.
• These advancements hold significant potential for applications in natural sciences, ecology, economics, and sociology, improving both system diagnosis and prediction model design.