[Fractal dimension and histogram method: algorithm and some preliminary results of noise-like time series analysis]

Area of Science:

• Time series analysis
• Fractal geometry
• Statistical signal processing

Context:

• Traditional histogram methods for time series analysis rely on subjective expert interpretation of histogram shapes.
• Existing algorithms for fractal dimension determination may lack precision when applied to noisy or complex time series data.

Purpose:

• To develop a robust methodological background for histogram-based time series analysis.
• To establish a connection between the shapes of smoothed histograms derived from time series segments and their fractal dimensions.
• To propose an advanced algorithm for precise fractal dimension determination.

Summary:

• A novel approach is presented that connects the shapes of smoothed histograms from time series segments to their fractal dimensions.
• It is demonstrated that fractal dimension exhibits key properties analogous to the histogram method.
• An enhanced fractal dimension determination algorithm is proposed, utilizing an 'all possible combination' method for improved accuracy.

Impact:

• This method offers a more objective and precise alternative to expert-based histogram analysis for time series.
• It enables accurate analysis of noise-like time series, yielding results comparable to traditional expert-driven histogram methods.
• The developed algorithm advances the field of time series analysis and fractal dimension computation.