Perceive, Solve, Reason: Progressive Capability Formation in Time Series-LLMs

Time Series Large Language Models (TS-LLMs) have shown growing capabilities in perception, task solving, and reasoning, yet these abilities are typically studied independently. We organize TS-LLM capabilities into three stages—Perceive, Solve, and Reason, and investigate how they progressively develop under two representative alignment architectures. Experiments show that Perceive facilitates Solve, while the complete Perceive $\to$ Solve $\to$ Reason pathway yields the strongest reasoning performance, especially under limited reasoning supervision. We further find that ordered capability accumulation is more effective than mixed supervision, and that the formation process is affected by input format and stage maturity. Cross-layer representation analysis reveals that different capabilities are transferred through distinct network depths rather than simply accumulated. Moreover, local stage convergence does not necessarily indicate sufficient preparation for subsequent capability development. Based on these findings, we derive a progressive training strategy and build strong Pre-align and Post-align TS-LLMs, achieving the best overall performance under fair out-of-domain evaluation.