Classification and clustering of time series with data-driven fragmented statistics

Abstract This paper proposes two simple and interpretable discrepancy statistics for clustering time series, based on highly significant truncated autocorrelation and partial autocorrelation functions (HSTACF and HSTPACF). Rather than using the full set of autocorrelation coefficients, these methods aim to retain only those that are most useful for clustering purposes, reducing noise and emphasizing meaningful temporal dependencies. Non-intuitively, theoretical and simulation results show that limiting the maximum order of autocorrelation coefficients and filtering out non-highly significant coefficients reduces the noise and improves estimation for classification purposes. We conduct a systematic simulation study covering autoregressive, moving average, mixed ARMA, trend-stationary, short-memory, and long-memory models to evaluate the effect of significance thresholding on clustering accuracy. Results show that HSTACF and HSTPACF discrepancies provide practical improvements over conventional ACF-/PACF-based distances, particularly when applied with K-means clustering. Applications to macroeconomic and financial time series, including GDP growth, fertility rates, inflation, and military expenditure, provide clustering that are both interpretable and consistent with established economic and demographic patterns. The proposed framework is computationally light, transparent, and broadly applicable, offering a practical refinement to time series clustering methodology.