Web-connected sensing applications continuously generate multivariate time series with evolving behavioral categories, making Time Series Class-Incremental Learning (TSCIL) essential for adapting to new classes without forgetting previously acquired knowledge. However, preserving diverse and evolving class distributions under strict privacy and memory constraints remains a fundamental challenge. Existing approaches often face a trade-off between retaining sufficient historical knowledge for accurate recognition and minimizing the memory required for continual adaptation. To address these limitations, we propose TRACE, a memory-efficient, replay-free framework that preserves class-specific knowledge through generative modeling rather than sample rehearsal. TRACE employs a compact, frozen temporal-spectral representation and lightweight class-specific autoencoders to capture complex intra-class variations. By independently preserving each class model, TRACE avoids recursive generation and catastrophic forgetting, while enabling direct classification through reconstruction-based scoring without retaining historical samples or large statistical matrices. Extensive experiments across five TSCIL benchmarks demonstrate that TRACE achieves competitive classification accuracy while reducing mean retained memory by approximately 98.26% compared with TS-ACL, the strongest evaluated analytical baseline, and achieving an approximately 33.43% relative improvement in accuracy on GrabMyo.

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