Time-Delay Identification Using Multiscale Ordinal Quantifiers

Area of Science:

• Complex Systems Analysis
• Time Series Analysis
• Nonlinear Dynamics

Background:

• Real-world systems often exhibit time-delayed interactions due to finite propagation speeds.
• The time scales of these interactions are frequently unknown and require inference from observed data.

Purpose of the Study:

• To explore ordinal-based quantifiers for identifying time-delays in time series data.
• To introduce a novel ordinal-based quantifier sensitive to nonlinearities.
• To compare the effectiveness of different quantifiers and standard methods.

Main Methods:

• Generation of artificial time series from stochastic and deterministic time-delay models.
• Application and comparison of various ordinal-based quantifiers.
• Utilizing the autocorrelation function for complementary analysis.
• Validation with real-world data from the North Atlantic Oscillation.

Main Results:

• Nonlinearities in generating models affect ordinal pattern distributions and delay identification quality.
• A novel ordinal-based quantifier demonstrates particular sensitivity to nonlinearities.
• The complementary use of ordinal quantifiers and autocorrelation function enhances time-delay identification.

Conclusions:

• Ordinal-based quantifiers are valuable tools for time-delay identification from time series.
• The proposed novel quantifier effectively captures nonlinear effects.
• Combining ordinal methods with autocorrelation provides robust time-delay estimation, validated on real-world atmospheric data.