Adaptive Segmentation and Statistical Analysis for Multivariate Big Data Forecasting

Forecasting high-volume, univariate, and multivariate longitudinal data streams is a critical challenge in Big Data systems, especially with constrained computational resources and pronounced data variability. However, existing approaches often neglect multivariate statistical complexity (e.g., covariance, skewness, kurtosis) of multivariate time series or rely on recency-only windowing that discards informative historical fluctuation patterns, limiting robustness under strict resource budgets. This work makes two core contributions to big data forecasting. First, we establish a formal, multi-dimensional framework for quantifying “data bigness” across statistical, computational, and algorithmic complexities, providing a rigorous foundation for analyzing resource-constrained problems. Second, guided by this framework, we extend and validate the Adaptive High-Fluctuation Recursive Segmentation (AHFRS) algorithm for multivariate time series. By incorporating higher-order statistics such as covariance, skewness, and kurtosis, AHFRS improves predictive accuracy under strict computational budgets. We validate the approach in two stages. First, a real-world case study on a univariate Bitcoin time series provides a practical stress test using a Long Short-Term Memory (LSTM) network as a robust baseline. This validation reveals a significant increase in forecasting robustness, with our method reducing the Root Mean Squared Error (RMSE) by more than 76% in a challenging scenario. Second, its generalizability is established on synthetic multivariate data sets in Finance, Retail, and Healthcare using standard statistical models. Across domains, AHFRS consistently outperforms baselines; in our multivariate Finance simulation, RMSE decreases by up to 62.5% in Finance and Mean Absolute Percentage Error (MAPE) drops by more than 10 percentage points in Healthcare. These results demonstrate that the proposed framework and AHFRS advances the theoretical modeling of data complexity and the design of adaptive, resource-efficient forecasting pipelines for real-world, high-volume data ecosystems.