Continuous Vs Discontinuous Data Imputation In Connected Complex Time Series: A Topological And Chaos Theory Framework With Evidence From U.S. Real Gdp Growth

This research evaluates the validity of continuous versus discontinuous data imputation techniques in connected complex time series by developing a methodological framework that integrates topological analysis and chaos theory. Using U.S. Real GDP quarterly growth from 1996 to 2024 as study case, we demonstrate that the time series exhibits characteristics of a chaotic system with high sensitivity to initial conditions and possesses a connected topology. Our findings reveal that continuous imputation techniques preserve essential topological properties while discontinuous methods fundamentally alter the system's structure, evidencing that unpredictability is ontologically inherent in this type of time series. This is supported by two key findings: first, the persistence of extreme fluctuations under continuous transformations and maintenance of global volatility patterns; second, the persistence of significant uncertainty across 14 machine and deep learning models after applying optimized Yeo-Johnson transformations. The results suggest that discontinuous imputation techniques may invalidate subsequent analysis by disrupting fundamental topological properties. Our research establishes a theoretical framework for evaluating imputation techniques based on mathematical properties of chaotic systems and general topology, providing practical guidance for handling extreme rare values in connected complex time series.