Recent advances in large language models (LLMs) have given rise to time-series question answering (TSQA), which formulates time-series analysis as natural-language question answering. However, directly feeding raw numerical series into LLMs suffers from a tokenization bottleneck: Byte Pair Encoding fragments continuous values into unstable tokens whose embeddings lack meaningful metric structure, resulting in the loss of magnitude, scale, and trend information. Prior methods use patch-based encoders that split the series into fixed windows, locking in one granularity that breaks patterns and hides exact timesteps, through a separate module that rarely transfers across datasets with different lengths or sampling rates. To address this challenge, we propose CADE (Contrastive Alignment with Direct Embedding), a novel framework for TSQA built upon two key components: direct timestep embedding and semantic alignment. The proposed framework maps each timestep directly into the LLM embedding space through a point-wise linear encoder and MLP projector, preserving exact index-level access while eliminating the need for patching and padding. To further bridge the semantic gap between time-series and language representations, we introduce a novel one-directional supervised contrastive loss that aligns time-series embeddings with frozen class-name text anchors. Experimental results on the public Time-MQA benchmark demonstrate that our framework consistently improves performance across six TSQA tasks, outperforming both open-source and proprietary LLM baselines.
Large language models (LLMs) and time-series language models (TSLMs) are increasingly applied to time-series question answering (TSQA). Unlike text-only QA, TSQA requires models to ground answers in temporal signals whose patterns may occur at different scales, specific time locations, or across separated intervals. However, existing benchmarks are typically organized by task types or high-level reasoning categories, making it difficult to diagnose the underlying signal-level capabilities driving model performance. We introduce TS-Skill, a controlled benchmark for evaluating three composable analytical skills in TSQA: temporal scale selection (SK1), temporal localization (SK2), and cross-interval integration (SK3). TS-Skill provides timestamp-aware questions, broad domain coverage, and human-validated QA quality. To construct the benchmark at scale, we develop SKEvol, a skill-guided agentic framework that combines domain-aware time-series seed generation, skill-controlled question generation, metadata- and code-assisted answer construction, multi-phase signal-grounded verification, and human-in-the-loop curation. Experiments on ten state-of-the-art LLMs and TSLMs reveal substantial and uneven capability gaps across SK1-SK3. In particular, SK3 remains consistently challenging for non-agent models, whereas tool-augmented agents show a selective advantage on standalone SK3. These findings demonstrate that skill-level evaluation can uncover temporal reasoning failures that are obscured by aggregate TSQA scores.
Token-based time series large language models (TS-LLMs) have emerged as a promising direction for time series analysis and reasoning. However, prior studies largely overlook the inherent continuity and ordinality of time series tokens, which substantially limits model performance. In this paper, we argue that preserving these properties in time series token embeddings is crucial for the effectiveness of token-based TS-LLMs. To this end, we propose COM (Continuity and Ordinality Matter), a continuity- and ordinality-aware strategy that integrates geometric constraints into both the initialization and training stages. Empirical results on multiple time series analysis benchmarks demonstrate that COM consistently improves the performance of token-based TS-LLMs, achieving competitive results and strong generalizability. Code is available at https://anonymous.4open.science/r/COM .
Large language models (LLMs) have demonstrated strong reasoning and instruction-following capabilities, making them potentially powerful tools for time-series analysis. However, time series lie outside their native textual modality, raising a fundamental question: how should time series be represented so that LLMs can reason about them effectively? Existing work typically serializes raw numerical sequences or fine-tunes pre-trained LLMs on time-series data. These approaches place the burden of extracting temporal structure directly on the LLM, creating a modality mismatch that often degrades performance on long sequences and introduces substantial computational overhead. In this work, we introduce Time-Series-to-Structured-Program representation (T2SP), a deterministic, training-free method that represents a time series as a structured symbolic program. T2SP decomposes time series into trends, periods, and salient events, expressing them in a program-friendly format aligned with the textual and code-like modalities on which LLMs are natively trained. By shifting temporal-structure extraction from the model to the representation itself, T2SP enables off-the-shelf LLMs to leverage their existing reasoning capabilities for time-series understanding. We evaluate T2SP on three reasoning tasks -- editing, captioning, and question answering -- where it consistently improves performance, reduces reasoning time, and lowers failure rates compared with raw-string representations. Our results demonstrate that T2SP provides an effective interface between time series and LLMs.