In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series data have high frequencies. The objective is to determine whether they follow a Gaussian or Lévy distribution, as well as establish the existence of long-range correlations in these time series. The results obtained from the DEA technique are compared with the Hurst R/S analysis and Detrended Fluctuation Analysis (DFA) methodologies. We conclude that these methodologies are effective in classifying the high frequency financial indices and volcanic eruption data—the financial time series can be characterized by a Lévy walk while the volcanic time series is characterized by a Lévy flight.

Time-series classification remains a critical task across various domains, demanding models that effectively capture both local recurrence structures and global temporal dependencies. We introduce a novel framework that transforms time series into image representations by fusing recurrence plots (RPs) with both Gramian Angular Summation Fields (GASFs) and Gramian Angular Difference Fields (GADFs). This fusion enriches the structural encoding of temporal dynamics. To ensure optimal performance, Bayesian Optimization is employed to automatically select the ideal image resolution, eliminating the need for manual tuning. Unlike prior methods that rely on individual transformations, our approach concatenates RP, GASF, and GADF into a unified representation and generalizes to multivariate data by stacking transformation channels across sensor dimensions. Experiments on seven univariate datasets show that our method significantly outperforms traditional classifiers such as one-nearest neighbor with Dynamic Time Warping, Shapelet Transform, and RP-based convolutional neural networks. For multivariate tasks, the proposed fusion model achieves macro F1 scores of 91.55% on the UCI Human Activity Recognition dataset and 98.95% on the UCI Room Occupancy Estimation dataset, outperforming standard deep learning baselines. These results demonstrate the robustness and generalizability of our framework, establishing a new benchmark for image-based time-series classification through principled fusion and adaptive optimization.