Predicting rainfall effectively requires an understanding of the predictability of the rainfall time series, often evaluated using the Hurst exponent value. The Hurst exponent value provides insights into the long-term memory of the time series, with values ranging between 0 and 1. Time series with Hurst exponent value near 0.5 exhibit poor predictability, while those with Hurst exponent near 1 or 0 indicate stronger predictability. However, previous research has shown that the Hurst exponent does not always accurately reflect the predictability of a series due to various underlying factors. This study investigates the limitations of the Hurst exponent in communicating predictability by incorporating additional analyses. Monthly rainfall time series data from 2000 to 2023 were analyzed for two contrasting regions: an arid region (Srivilliputtur, Tamil Nadu, India) and a high-rainfall region (Alappuzha, Kerala, India). The calculated Hurst exponents for these regions were 0.70 and 0.48, respectively, suggesting better predictability for the arid region compared to the high-rainfall region. However, predictions made using an Artificial Neural Network (ANN) contradicted these findings, with 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 latter. To explore this discrepancy, the study examined short-term memory effects through the Auto-Correlation Function (ACF) up to 12 lags. Results revealed that the ACF significance was stronger for the high-rainfall region (10 lags) compared to the arid region (3 lags), suggesting that short-term memory impacts the Hurst exponent’s effectiveness in assessing predictability. These findings indicate that while long-term trends, represented by the Hurst exponent are important, short-term fluctuations captured through ACF, can significantly influence prediction accuracy. The study concludes that relying solely on the Hurst exponent to evaluate predictability may not lead to correct conclusions, especially in cases where short-term memory effects dominate. A combined analysis of both long-term trends (Hurst exponent) and short-term dependencies (ACF) is recommended to improve the assessment of rainfall time series predictability.