Clustering time series based on dependence structure.

Area of Science:

• Statistics
• Data Science
• Machine Learning

Background:

• Traditional time series clustering often assumes linear dependencies, which is frequently inadequate for real-world data.
• Existing methods struggle with complex, non-linear relationships within time series.

Purpose of the Study:

• To develop and validate a novel clustering approach for time series exhibiting general and dependent structures.
• To address the limitations of linear dependency assumptions in time series analysis.

Main Methods:

• Proposing a copula-based distance measure to quantify dissimilarity between time series.
• Developing a strongly consistent estimator for the proposed copula-based distance.
• Applying a hierarchical clustering algorithm to the computed distance matrix for grouping time series.

Main Results:

• The proposed copula-based distance estimator is shown to be strongly consistent.
• Numerical simulations and real-world data analysis demonstrate the effectiveness of the clustering method.
• The approach successfully clusters time series with general and dependent structures.

Conclusions:

• The copula-based distance offers a robust alternative for time series clustering when linear assumptions fail.
• This method enhances the ability to uncover underlying patterns in complex time series data.
• The validated approach provides a reliable tool for diverse applications requiring time series analysis.