Saravanan et al. (2026) An Investigation on the Relationship Between Hurst Exponent and Short-Term Memory in Rainfall Time Series

Identification

• Journal: Lecture notes in civil engineering
• Year: 2026
• Date: 2026-01-01
• Authors: P. Saravanan, C. Sivapragasam
• DOI: 10.1007/978-3-032-04149-4_24

Research Groups

• Department of Civil Engineering, Dr. Ambedkar Institute of Technology, Bengaluru, India
• Department of Civil Engineering, Kalasalingam Academy of Research and Education, Srivilliputtur, India

Short Summary

This study investigates the limitations of the Hurst exponent in assessing rainfall predictability by incorporating short-term memory analysis, concluding that a combined approach of Hurst exponent and Auto-Correlation Function is necessary for accurate evaluation.

Objective

• To investigate the limitations of the Hurst exponent in accurately communicating the predictability of rainfall time series.
• To explore the influence of short-term memory effects, as measured by the Auto-Correlation Function (ACF), on the effectiveness of the Hurst exponent in assessing predictability.

Study Configuration

• Spatial Scale: Two contrasting regions in India: Srivilliputtur, Tamil Nadu (arid region) and Alappuzha, Kerala (high-rainfall region).
• Temporal Scale: Monthly rainfall time series data from 2000 to 2023 (23 years).

Methodology and Data

• Models used:
  • Hurst exponent calculation for long-term memory assessment.
  • Artificial Neural Network (ANN) for rainfall prediction, evaluated using Normalized Root Mean Square Error (NRMSE).
  • Auto-Correlation Function (ACF) up to 12 lags for short-term memory analysis.
• Data sources: Monthly rainfall time series data from observation stations in the selected regions.

Main Results

• The calculated Hurst exponents were 0.70 for the arid region and 0.48 for the high-rainfall region, suggesting better predictability for the arid region based on long-term memory.
• Artificial Neural Network (ANN) predictions showed Normalized Root Mean Square Errors (NRMSE) of 0.807 for the arid region and 0.283 for the high-rainfall region, indicating better prediction accuracy for the high-rainfall region.
• This discrepancy highlighted that the Hurst exponent alone did not accurately reflect predictability.
• Short-term memory analysis using ACF revealed stronger significance for the high-rainfall region (10 lags) compared to the arid region (3 lags).
• The study concluded that short-term memory significantly impacts the Hurst exponent's effectiveness in assessing predictability, and a combined analysis of both long-term trends (Hurst exponent) and short-term dependencies (ACF) is recommended for improved assessment.

Contributions

• Demonstrates empirically that relying solely on the Hurst exponent can lead to incorrect conclusions regarding rainfall time series predictability.
• Highlights the critical role of short-term memory, quantified by the Auto-Correlation Function, in influencing overall prediction accuracy, especially when it contradicts long-term memory indicators.
• Proposes a more robust approach for assessing rainfall predictability by advocating for a combined analysis of both Hurst exponent and Auto-Correlation Function.

Funding

• Not explicitly mentioned in the provided text.

Citation

@article{Saravanan2026Investigation,
  author = {Saravanan, P. and Sivapragasam, C.},
  title = {An Investigation on the Relationship Between Hurst Exponent and Short-Term Memory in Rainfall Time Series},
  journal = {Lecture notes in civil engineering},
  year = {2026},
  doi = {10.1007/978-3-032-04149-4_24},
  url = {https://doi.org/10.1007/978-3-032-04149-4_24}
}